[2170] | 1 | include "ASM/AssemblyProof.ma". |
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| 2 | include alias "arithmetics/nat.ma". |
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| 3 | include alias "basics/logic.ma". |
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| 4 | |
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| 5 | lemma set_arg_16_mk_Status_commutation: |
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| 6 | ∀M: Type[0]. |
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| 7 | ∀cm: M. |
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| 8 | ∀s: PreStatus M cm. |
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| 9 | ∀w: Word. |
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| 10 | ∀d: [[dptr]]. |
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| 11 | set_arg_16 M cm s w d = |
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| 12 | mk_PreStatus M cm |
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| 13 | (low_internal_ram … s) |
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| 14 | (high_internal_ram … s) |
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| 15 | (external_ram … s) |
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| 16 | (program_counter … s) |
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| 17 | (special_function_registers_8051 … (set_arg_16 M cm s w d)) |
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| 18 | (special_function_registers_8052 … s) |
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| 19 | (p1_latch … s) |
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| 20 | (p3_latch … s) |
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| 21 | (clock … s). |
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| 22 | #M #cm #s #w #d |
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| 23 | whd in match set_arg_16; normalize nodelta |
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| 24 | whd in match set_arg_16'; normalize nodelta |
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| 25 | @(subaddressing_mode_elim … d) |
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| 26 | cases (vsplit bool 8 8 w) #bu #bl normalize nodelta |
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| 27 | whd in match set_8051_sfr; normalize nodelta % |
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| 28 | qed. |
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| 29 | |
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| 30 | lemma set_program_counter_mk_Status_commutation: |
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| 31 | ∀M: Type[0]. |
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| 32 | ∀cm: M. |
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| 33 | ∀s: PreStatus M cm. |
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| 34 | ∀w: Word. |
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| 35 | set_program_counter M cm s w = |
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| 36 | mk_PreStatus M cm |
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| 37 | (low_internal_ram … s) |
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| 38 | (high_internal_ram … s) |
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| 39 | (external_ram … s) |
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| 40 | w |
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| 41 | (special_function_registers_8051 … s) |
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| 42 | (special_function_registers_8052 … s) |
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| 43 | (p1_latch … s) |
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| 44 | (p3_latch … s) |
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| 45 | (clock … s). |
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| 46 | // |
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| 47 | qed. |
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| 48 | |
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| 49 | lemma set_clock_mk_Status_commutation: |
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| 50 | ∀M: Type[0]. |
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| 51 | ∀cm: M. |
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| 52 | ∀s: PreStatus M cm. |
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| 53 | ∀c: nat. |
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| 54 | set_clock M cm s c = |
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| 55 | mk_PreStatus M cm |
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| 56 | (low_internal_ram … s) |
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| 57 | (high_internal_ram … s) |
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| 58 | (external_ram … s) |
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| 59 | (program_counter … s) |
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| 60 | (special_function_registers_8051 … s) |
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| 61 | (special_function_registers_8052 … s) |
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| 62 | (p1_latch … s) |
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| 63 | (p3_latch … s) |
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| 64 | c. |
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| 65 | // |
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| 66 | qed. |
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| 67 | |
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| 68 | lemma get_8051_sfr_set_clock: |
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| 69 | ∀M: Type[0]. |
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| 70 | ∀cm: M. |
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| 71 | ∀s: PreStatus M cm. |
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| 72 | ∀sfr: SFR8051. |
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| 73 | ∀t: Time. |
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| 74 | get_8051_sfr M cm (set_clock M cm s t) sfr = |
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| 75 | get_8051_sfr M cm s sfr. |
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| 76 | #M #cm #s #sfr #t % |
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| 77 | qed. |
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| 78 | |
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| 79 | lemma get_8051_sfr_set_program_counter: |
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| 80 | ∀M: Type[0]. |
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| 81 | ∀cm: M. |
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| 82 | ∀s: PreStatus M cm. |
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| 83 | ∀sfr: SFR8051. |
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| 84 | ∀pc: Word. |
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| 85 | get_8051_sfr M cm (set_program_counter M cm s pc) = |
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| 86 | get_8051_sfr M cm s. |
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| 87 | #M #cm #s #sfr #pc % |
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| 88 | qed. |
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| 89 | |
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| 90 | lemma special_function_registers_8051_set_arg_16: |
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| 91 | ∀M, M': Type[0]. |
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| 92 | ∀cm: M. |
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| 93 | ∀cm': M'. |
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| 94 | ∀s: PreStatus M cm. |
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| 95 | ∀s': PreStatus M' cm'. |
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| 96 | ∀w, w': Word. |
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| 97 | ∀d, d': [[dptr]]. |
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| 98 | special_function_registers_8051 ?? s = special_function_registers_8051 … s' → |
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| 99 | w = w' → |
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| 100 | special_function_registers_8051 ?? (set_arg_16 … s w d) = |
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| 101 | special_function_registers_8051 ?? (set_arg_16 M' cm' s' w' d'). |
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| 102 | #M #M' #cm #cm' #s #s' #w #w' |
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| 103 | #d @(subaddressing_mode_elim … d) |
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| 104 | #d' @(subaddressing_mode_elim … d') |
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| 105 | #EQ1 #EQ2 <EQ2 normalize cases (vsplit bool 8 8 w) #b1 #b2 normalize <EQ1 % |
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| 106 | qed. |
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| 107 | |
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| 108 | lemma program_counter_set_arg_1: |
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| 109 | ∀M: Type[0]. |
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| 110 | ∀cm: M. |
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| 111 | ∀s: PreStatus M cm. |
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| 112 | ∀addr: [[bit_addr; carry]]. |
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| 113 | ∀b: Bit. |
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| 114 | program_counter M cm (set_arg_1 M cm s addr b) = program_counter M cm s. |
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| 115 | #M #cm #s whd in match set_arg_1; whd in match set_arg_1'; normalize nodelta |
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| 116 | #addr #b |
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| 117 | @(subaddressing_mode_elim … addr) |
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| 118 | [1: |
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| 119 | #byte cases (vsplit ????) #nu #nl normalize nodelta |
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| 120 | cases (vsplit ????) #ignore #three_bits normalize nodelta |
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| 121 | cases (get_index_v bool ????) normalize nodelta |
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| 122 | [1: |
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| 123 | @program_counter_set_bit_addressable_sfr |
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| 124 | |2: |
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| 125 | @program_counter_set_low_internal_ram |
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| 126 | ] |
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| 127 | |2: |
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| 128 | cases (vsplit ????) // |
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| 129 | ] |
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| 130 | qed. |
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| 131 | |
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| 132 | lemma get_ov_flag_set_program_counter: |
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| 133 | ∀M: Type[0]. |
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| 134 | ∀cm: M. |
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| 135 | ∀s: PreStatus M cm. |
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| 136 | ∀pc: Word. |
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| 137 | get_ov_flag M cm (set_program_counter M cm s pc) = |
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| 138 | get_ov_flag M cm s. |
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| 139 | #M #cm #s #pc % |
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| 140 | qed. |
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| 141 | |
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| 142 | lemma external_ram_set_program_counter: |
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| 143 | ∀M: Type[0]. |
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| 144 | ∀cm: M. |
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| 145 | ∀s: PreStatus M cm. |
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| 146 | ∀pc: Word. |
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| 147 | external_ram M cm (set_program_counter M cm s pc) = |
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| 148 | external_ram M cm s. |
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| 149 | #M #cm #s #pc % |
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| 150 | qed. |
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| 151 | |
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| 152 | lemma low_internal_ram_set_program_counter: |
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| 153 | ∀M: Type[0]. |
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| 154 | ∀cm: M. |
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| 155 | ∀s: PreStatus M cm. |
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| 156 | ∀pc: Word. |
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| 157 | low_internal_ram M cm (set_program_counter M cm s pc) = |
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| 158 | low_internal_ram M cm s. |
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| 159 | #M #cm #s #pc % |
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| 160 | qed. |
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| 161 | |
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| 162 | lemma high_internal_ram_set_program_counter: |
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| 163 | ∀M: Type[0]. |
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| 164 | ∀cm: M. |
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| 165 | ∀s: PreStatus M cm. |
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| 166 | ∀pc: Word. |
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| 167 | high_internal_ram M cm (set_program_counter M cm s pc) = |
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| 168 | high_internal_ram M cm s. |
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| 169 | #M #cm #s #pc % |
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| 170 | qed. |
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| 171 | |
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| 172 | lemma get_arg_8_set_program_counter: |
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| 173 | ∀M: Type[0]. |
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| 174 | ∀cm: M. |
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| 175 | ∀s: PreStatus M cm. |
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| 176 | ∀flag: bool. |
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| 177 | ∀addr: [[direct; indirect; registr; acc_a; acc_b; data; acc_dptr; ext_indirect; ext_indirect_dptr]]. |
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| 178 | ∀pc: Word. |
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| 179 | get_arg_8 M cm (set_program_counter M cm s pc) flag addr = |
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| 180 | get_arg_8 M cm s flag addr. |
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| 181 | [2,3: |
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| 182 | cases addr #subaddressing_mode |
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| 183 | cases subaddressing_mode |
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| 184 | try (#addr1 whd in ⊢ (% → %);) |
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| 185 | whd in ⊢ (% → %); // |
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| 186 | ] |
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| 187 | #M #cm #s #flag #addr #pc |
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| 188 | whd in match get_arg_8; normalize nodelta |
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| 189 | cases addr * |
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| 190 | try (#addr1 #absurd normalize in absurd; cases absurd @I) |
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| 191 | try (#absurd normalize in absurd; cases absurd @I) |
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| 192 | try (#addr1 #addr2) try #addr1 |
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| 193 | normalize nodelta % |
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| 194 | qed. |
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| 195 | |
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| 196 | lemma external_ram_set_flags: |
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| 197 | ∀M: Type[0]. |
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| 198 | ∀cm: M. |
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| 199 | ∀s: PreStatus M cm. |
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| 200 | ∀opt: option Bit. |
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| 201 | ∀bit1, bit2: Bit. |
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| 202 | external_ram M cm (set_flags M cm s bit1 opt bit2) = |
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| 203 | external_ram M cm s. |
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| 204 | #M #cm #s #opt #bit1 #bit2 % |
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| 205 | qed. |
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| 206 | |
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| 207 | lemma low_internal_ram_set_flags: |
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| 208 | ∀M: Type[0]. |
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| 209 | ∀cm: M. |
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| 210 | ∀s: PreStatus M cm. |
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| 211 | ∀opt: option Bit. |
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| 212 | ∀bit1, bit2: Bit. |
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| 213 | low_internal_ram M cm (set_flags M cm s bit1 opt bit2) = |
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| 214 | low_internal_ram M cm s. |
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| 215 | #M #cm #s #opt #bit1 #bit2 % |
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| 216 | qed. |
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| 217 | |
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| 218 | lemma high_internal_ram_set_flags: |
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| 219 | ∀M: Type[0]. |
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| 220 | ∀cm: M. |
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| 221 | ∀s: PreStatus M cm. |
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| 222 | ∀opt: option Bit. |
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| 223 | ∀bit1, bit2: Bit. |
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| 224 | high_internal_ram M cm (set_flags M cm s bit1 opt bit2) = |
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| 225 | high_internal_ram M cm s. |
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| 226 | #M #cm #s #opt #bit1 #bit2 % |
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| 227 | qed. |
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| 228 | |
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| 229 | lemma low_internal_ram_set_clock: |
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| 230 | ∀M: Type[0]. |
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| 231 | ∀cm: M. |
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| 232 | ∀s: PreStatus M cm. |
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| 233 | ∀t: Time. |
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| 234 | low_internal_ram M cm (set_clock M cm s t) = |
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| 235 | low_internal_ram M cm s. |
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| 236 | #M #cm #s #t % |
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| 237 | qed. |
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| 238 | |
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| 239 | lemma high_internal_ram_set_clock: |
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| 240 | ∀M: Type[0]. |
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| 241 | ∀cm: M. |
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| 242 | ∀s: PreStatus M cm. |
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| 243 | ∀t: Time. |
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| 244 | high_internal_ram M cm (set_clock M cm s t) = |
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| 245 | high_internal_ram M cm s. |
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| 246 | #M #cm #s #t % |
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| 247 | qed. |
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| 248 | |
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| 249 | lemma external_ram_set_clock: |
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| 250 | ∀M: Type[0]. |
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| 251 | ∀cm: M. |
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| 252 | ∀s: PreStatus M cm. |
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| 253 | ∀t: Time. |
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| 254 | external_ram M cm (set_clock M cm s t) = |
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| 255 | external_ram M cm s. |
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| 256 | #M #cm #s #t % |
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| 257 | qed. |
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| 258 | |
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| 259 | lemma set_8051_sfr_set_program_counter: |
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| 260 | ∀M: Type[0]. |
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| 261 | ∀cm: M. |
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| 262 | ∀s: PreStatus M cm. |
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| 263 | ∀pc: Word. |
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| 264 | ∀sfr: SFR8051. |
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| 265 | ∀v: Byte. |
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| 266 | set_8051_sfr M cm (set_program_counter M cm s pc) sfr v = |
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| 267 | set_program_counter M cm (set_8051_sfr M cm s sfr v) pc. |
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| 268 | #M #cm #s #pc #sfr #v % |
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| 269 | qed. |
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| 270 | |
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| 271 | lemma low_internal_ram_set_8051_sfr: |
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| 272 | ∀M: Type[0]. |
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| 273 | ∀cm: M. |
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| 274 | ∀s: PreStatus M cm. |
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| 275 | ∀sfr: SFR8051. |
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| 276 | ∀v: Byte. |
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| 277 | low_internal_ram M cm (set_8051_sfr M cm s sfr v) = |
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| 278 | low_internal_ram M cm s. |
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| 279 | #M #cm #s #sfr #v % |
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| 280 | qed. |
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| 281 | |
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| 282 | lemma high_internal_ram_set_8051_sfr: |
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| 283 | ∀M: Type[0]. |
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| 284 | ∀cm: M. |
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| 285 | ∀s: PreStatus M cm. |
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| 286 | ∀sfr: SFR8051. |
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| 287 | ∀v: Byte. |
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| 288 | high_internal_ram M cm (set_8051_sfr M cm s sfr v) = |
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| 289 | high_internal_ram M cm s. |
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| 290 | #M #cm #s #sfr #v % |
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| 291 | qed. |
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| 292 | |
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| 293 | lemma external_ram_set_8051_sfr: |
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| 294 | ∀M: Type[0]. |
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| 295 | ∀cm: M. |
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| 296 | ∀s: PreStatus M cm. |
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| 297 | ∀sfr: SFR8051. |
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| 298 | ∀v: Byte. |
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| 299 | external_ram M cm (set_8051_sfr M cm s sfr v) = |
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| 300 | external_ram M cm s. |
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| 301 | #M #cm #s #sfr #v % |
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| 302 | qed. |
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| 303 | |
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| 304 | lemma get_arg_8_set_clock: |
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| 305 | ∀M: Type[0]. |
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| 306 | ∀cm: M. |
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| 307 | ∀s: PreStatus M cm. |
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| 308 | ∀addr. |
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| 309 | ∀t: Time. |
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| 310 | get_arg_8 M cm (set_clock M cm s t) addr = |
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| 311 | get_arg_8 M cm s addr. |
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| 312 | #M #cm #s #addr #t % |
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| 313 | qed. |
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| 314 | |
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| 315 | lemma set_program_counter_set_program_counter: |
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| 316 | ∀M: Type[0]. |
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| 317 | ∀cm: M. |
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| 318 | ∀s: PreStatus M cm. |
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| 319 | ∀pc: Word. |
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| 320 | ∀pc': Word. |
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| 321 | set_program_counter M cm (set_program_counter M cm s pc) pc' = |
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| 322 | set_program_counter M cm s pc'. |
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| 323 | #M #cm #s #pc #pc' % |
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| 324 | qed. |
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| 325 | |
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| 326 | (* XXX: move elsewhere *) |
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| 327 | lemma bitvector_8_cases: |
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| 328 | ∀w: BitVector 8. |
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| 329 | ∃b0,b1,b2,b3,b4,b5,b6,b7: bool. |
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| 330 | w ≃ [[b0;b1;b2;b3;b4;b5;b6;b7]]. |
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| 331 | #w repeat (cases (BitVector_Sn … w) #b0 * #w0 #EQ0 >EQ0 %{b0} -w lapply w0 -w0 #w) |
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| 332 | >(BitVector_O … w) % |
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| 333 | qed. |
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| 334 | |
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| 335 | (* XXX: not true |
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| 336 | lemma p3_latch_set_arg_8: |
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| 337 | ∀M: Type[0]. |
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| 338 | ∀cm: M. |
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| 339 | ∀s: PreStatus M cm. |
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| 340 | ∀args. |
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| 341 | ∀v: Byte. |
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| 342 | p3_latch M cm (set_arg_8 M cm s args v) = |
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| 343 | p3_latch M cm s. |
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| 344 | #M #cm #s #args #v |
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| 345 | @(subaddressing_mode_elim … args) |
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| 346 | try #w try % |
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| 347 | whd in match set_arg_8; normalize nodelta |
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| 348 | whd in match set_arg_8'; normalize nodelta |
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| 349 | inversion (vsplit bool ???) #nu #nl #nu_nl_refl normalize nodelta |
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| 350 | inversion (vsplit bool ???) #ignore #three_bits #ignore_three_bits_refl normalize nodelta |
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| 351 | inversion (get_index_v bool ????) #get_index_v_refl normalize nodelta try % |
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| 352 | whd in match set_bit_addressable_sfr; normalize nodelta |
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| 353 | @(bitvector_8_elim_prop … w) |
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| 354 | *) |
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| 355 | |
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| 356 | lemma status_of_pseudo_status_does_not_change_8051_sfrs: |
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| 357 | ∀M: internal_pseudo_address_map. |
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| 358 | ∀cm: pseudo_assembly_program. |
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| 359 | ∀s: PreStatus pseudo_assembly_program cm. |
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| 360 | ∀sigma: Word → Word. |
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| 361 | ∀policy: Word → bool. |
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| 362 | \snd M = data → |
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| 363 | special_function_registers_8051 pseudo_assembly_program cm s = |
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| 364 | special_function_registers_8051 (BitVectorTrie Byte 16) |
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| 365 | (code_memory_of_pseudo_assembly_program cm sigma policy) |
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| 366 | (status_of_pseudo_status M cm s sigma policy). |
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| 367 | #M #cm #s #sigma #policy #None_proof cases s |
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| 368 | #H1 #H2 #H3 #H4 #H5 #H6 #H7 #H8 #H9 |
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| 369 | whd in match status_of_pseudo_status; normalize nodelta |
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| 370 | whd in match sfr_8051_of_pseudo_sfr_8051; normalize nodelta |
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| 371 | >None_proof % |
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| 372 | qed. |
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| 373 | |
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| 374 | lemma n_lt_19_elim_prop: |
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| 375 | ∀P: nat → Prop. |
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| 376 | P 0 → P 1 → P 2 → P 3 → P 4 → P 5 → P 6 → P 7 → P 8 → P 9 → |
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| 377 | P 10 → P 11 → P 12 → P 13 → P 14 → P 15 → P 16 → P 17 → P 18 → |
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| 378 | (∀n. n < 19 → P n). |
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| 379 | #P #H1 #H2 #H3 #H4 #H5 #H6 #H7 #H8 #H9 #H10 #H11 #H12 #H13 #H14 |
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| 380 | #H15 #H16 #H17 #H18 #H19 #n |
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| 381 | cases n [1: // ] |
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| 382 | #n' cases n' [1: // ] #n' cases n' [1: // ] #n' cases n' [1: // ] |
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| 383 | #n' cases n' [1: // ] #n' cases n' [1: // ] #n' cases n' [1: // ] |
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| 384 | #n' cases n' [1: // ] #n' cases n' [1: // ] #n' cases n' [1: // ] |
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| 385 | #n' cases n' [1: // ] #n' cases n' [1: // ] #n' cases n' [1: // ] |
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| 386 | #n' cases n' [1: // ] #n' cases n' [1: // ] #n' cases n' [1: // ] |
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| 387 | #n' cases n' [1: // ] #n' cases n' [1: // ] #n' cases n' [1: // ] |
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| 388 | #n' normalize in ⊢ (% → ?); |
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| 389 | #absurd repeat (lapply (le_S_S_to_le … absurd) #absurd) |
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| 390 | cases (lt_to_not_zero … absurd) |
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| 391 | qed. |
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| 392 | |
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| 393 | lemma get_index_v_set_index_miss: |
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| 394 | ∀T: Type[0]. |
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| 395 | ∀n, i, j: nat. |
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| 396 | ∀v: Vector T n. |
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| 397 | ∀b: T. |
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| 398 | ∀i_proof: i < n. |
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| 399 | ∀j_proof: j < n. |
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| 400 | i ≠ j → |
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| 401 | get_index_v T n (set_index T n v i b i_proof) j j_proof = |
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| 402 | get_index_v T n v j j_proof. |
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| 403 | #T #n #i #j #v lapply i lapply j elim v #i #j |
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| 404 | [1: |
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| 405 | #b #i_proof |
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| 406 | cases (lt_to_not_zero … i_proof) |
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| 407 | |2: |
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| 408 | #tl #inductive_hypothesis #j' #i' #b #i_proof #j_proof #i_neq_j |
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| 409 | lapply i_proof lapply i_neq_j cases i' |
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| 410 | [1: |
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| 411 | -i_neq_j #i_neq_j -i_proof #i_proof |
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| 412 | whd in match (set_index ??????); |
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| 413 | lapply j_proof lapply i_neq_j cases j' |
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| 414 | [1: |
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| 415 | #relevant @⊥ cases relevant -relevant #absurd @absurd % |
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| 416 | |2: |
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| 417 | #j' #_ -j_proof #j_proof % |
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| 418 | ] |
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| 419 | |2: |
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| 420 | #i' -i_neq_j #i_neq_j -i_proof #i_proof |
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| 421 | lapply j_proof lapply i_neq_j cases j' |
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| 422 | [1: |
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| 423 | #_ #j_proof % |
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| 424 | |2: |
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| 425 | #j' #i_neq_j #j_proof |
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| 426 | @inductive_hypothesis @nmk #relevant |
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| 427 | cases i_neq_j #absurd @absurd >relevant % |
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| 428 | ] |
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| 429 | ] |
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| 430 | ] |
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| 431 | qed. |
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| 432 | |
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| 433 | lemma get_index_v_special_function_registers_8051_not_acc_a: |
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| 434 | ∀M: internal_pseudo_address_map. |
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| 435 | ∀cm: pseudo_assembly_program. |
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| 436 | ∀s: PreStatus pseudo_assembly_program cm. |
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| 437 | ∀sigma: Word → Word. |
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| 438 | ∀policy: Word → bool. |
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| 439 | ∀n: nat. |
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| 440 | ∀proof: n < 19. |
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| 441 | n ≠ 17 → |
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| 442 | (get_index_v Byte 19 |
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| 443 | (special_function_registers_8051 pseudo_assembly_program cm s) n |
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| 444 | proof = |
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| 445 | get_index_v Byte 19 |
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| 446 | (special_function_registers_8051 (BitVectorTrie Byte 16) |
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| 447 | (code_memory_of_pseudo_assembly_program cm sigma policy) |
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| 448 | (status_of_pseudo_status M cm s sigma policy)) n |
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| 449 | proof). |
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| 450 | #M #cm #s #sigma #policy #n #proof lapply proof |
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| 451 | @(n_lt_19_elim_prop … proof) -proof #proof |
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| 452 | [18: |
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| 453 | #absurd @⊥ cases absurd -absurd #absurd @absurd % |
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| 454 | ] |
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| 455 | #_ cases s #H1 #H2 #H3 #H4 #H5 #H6 #H7 #H8 #H9 |
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| 456 | whd in match status_of_pseudo_status; normalize nodelta |
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| 457 | whd in match sfr_8051_of_pseudo_sfr_8051; normalize nodelta |
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| 458 | cases M #left #right cases right normalize nodelta try % |
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| 459 | -right * #address |
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| 460 | @pair_elim #high #low #high_low_refl normalize nodelta |
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| 461 | whd in match sfr_8051_index; normalize nodelta |
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| 462 | >get_index_v_set_index_miss try % |
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| 463 | #absurd destruct(absurd) |
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| 464 | qed. |
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| 465 | |
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| 466 | (* |
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| 467 | include alias "arithmetics/nat.ma". |
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| 468 | include alias "basics/logic.ma". |
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| 469 | include alias "ASM/BitVectorTrie.ma". |
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| 470 | *) |
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| 471 | |
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| 472 | lemma get_8051_sfr_status_of_pseudo_status: |
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| 473 | ∀M. |
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| 474 | ∀cm, ps, sigma, policy. |
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| 475 | ∀sfr. |
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| 476 | (sfr = SFR_ACC_A → \snd M = data) → |
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| 477 | get_8051_sfr (BitVectorTrie Byte 16) |
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| 478 | (code_memory_of_pseudo_assembly_program cm sigma policy) |
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| 479 | (status_of_pseudo_status M cm ps sigma policy) sfr = |
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| 480 | get_8051_sfr pseudo_assembly_program cm ps sfr. |
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| 481 | #M #cm #ps #sigma #policy * cases M #fstM #sndM #relevant |
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| 482 | [18: |
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| 483 | >relevant % |
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| 484 | ] |
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| 485 | cases sndM try % * #address |
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| 486 | whd in match get_8051_sfr; |
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| 487 | whd in match status_of_pseudo_status; normalize nodelta |
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| 488 | whd in match sfr_8051_of_pseudo_sfr_8051; normalize nodelta |
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| 489 | @pair_elim #upper #lower #upper_lower_refl |
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| 490 | @get_index_v_set_index_miss @nmk #relevant |
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| 491 | normalize in relevant; destruct(relevant) |
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| 492 | qed. |
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| 493 | |
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| 494 | lemma bitvector_cases_hd_tl: |
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| 495 | ∀n: nat. |
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| 496 | ∀w: BitVector (S n). |
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| 497 | ∃hd: bool. ∃tl: BitVector n. |
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| 498 | w ≃ hd:::tl. |
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| 499 | #n #w cases (BitVector_Sn … w) #hd #relevant %{hd} @relevant |
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| 500 | qed. |
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| 501 | |
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| 502 | lemma external_ram_set_bit_addressable_sfr: |
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| 503 | ∀M: Type[0]. |
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| 504 | ∀cm: M. |
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| 505 | ∀ps. |
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| 506 | ∀w. |
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| 507 | ∀result: Byte. |
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| 508 | external_ram M cm |
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| 509 | (set_bit_addressable_sfr M cm ps w result) = |
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| 510 | external_ram M cm ps. |
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| 511 | #M #cm #ps #w #result cases daemon (* XXX: prove this with Russell in Status.ma! |
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| 512 | whd in match set_bit_addressable_sfr; normalize nodelta |
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| 513 | cases (eqb ??) normalize nodelta [1: cases not_implemented ] |
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| 514 | cases (eqb ??) normalize nodelta [1: % ] |
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| 515 | cases (eqb ??) normalize nodelta [1: cases not_implemented ] |
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| 516 | cases (eqb ??) normalize nodelta [1: % ] |
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| 517 | cases (eqb ??) normalize nodelta [1: % ] |
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| 518 | cases (eqb ??) normalize nodelta [1: % ] |
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| 519 | cases (eqb ??) normalize nodelta [1: % ] |
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| 520 | cases (eqb ??) normalize nodelta [1: % ] |
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| 521 | cases (eqb ??) normalize nodelta [1: % ] |
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| 522 | cases (eqb ??) normalize nodelta [1: % ] |
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| 523 | cases (eqb ??) normalize nodelta [1: % ] |
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| 524 | cases (eqb ??) normalize nodelta [1: % ] |
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| 525 | cases (eqb ??) normalize nodelta [1: % ] |
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| 526 | cases (eqb ??) normalize nodelta [1: % ] |
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| 527 | cases (eqb ??) normalize nodelta [1: % ] |
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| 528 | cases (eqb ??) normalize nodelta [1: % ] |
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| 529 | cases (eqb ??) normalize nodelta [1: % ] |
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| 530 | cases (eqb ??) normalize nodelta [1: % ] |
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| 531 | cases (eqb ??) normalize nodelta [1: % ] |
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| 532 | cases (eqb ??) normalize nodelta [1: % ] |
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| 533 | cases (eqb ??) normalize nodelta [1: % ] |
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| 534 | cases (eqb ??) normalize nodelta [1: % ] |
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| 535 | cases (eqb ??) normalize nodelta [1: % ] |
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| 536 | cases (eqb ??) normalize nodelta [1: % ] |
---|
| 537 | cases (eqb ??) normalize nodelta [1: % ] |
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| 538 | cases (eqb ??) normalize nodelta [1: % ] |
---|
| 539 | cases not_implemented *) |
---|
| 540 | qed. |
---|
| 541 | |
---|
| 542 | lemma external_ram_set_arg_8: |
---|
| 543 | ∀M: Type[0]. |
---|
| 544 | ∀cm: M. |
---|
| 545 | ∀ps. |
---|
| 546 | ∀addr1: [[direct; indirect; registr; acc_a; acc_b ]]. |
---|
| 547 | ∀result. |
---|
| 548 | external_ram M cm (set_arg_8 M cm ps addr1 result) = |
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| 549 | external_ram M cm ps. |
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| 550 | [2: /2 by is_in_subvector_is_in_supervector, subaddressing_modein, I/ ] |
---|
| 551 | #M #cm #ps #addr1 #result |
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| 552 | @(subaddressing_mode_elim … addr1) try #w try % |
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| 553 | whd in ⊢ (??(???%)?); whd in ⊢ (??(???(???%))?); (* XXX: to be understood, slow match *) |
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| 554 | [1: |
---|
| 555 | cases (vsplit bool ???) #nu #nl normalize nodelta |
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| 556 | cases (vsplit bool ???) #ignore #three_bits normalize nodelta |
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| 557 | cases (get_index_v bool ????) normalize nodelta try % |
---|
| 558 | @external_ram_set_bit_addressable_sfr |
---|
| 559 | |2: |
---|
| 560 | cases (vsplit bool ???) #nu #nl normalize nodelta |
---|
| 561 | cases (vsplit bool ???) #ignore #three_bits normalize nodelta |
---|
| 562 | cases (get_index_v bool ????) normalize nodelta % |
---|
| 563 | ] |
---|
| 564 | qed. |
---|
| 565 | |
---|
| 566 | lemma special_function_registers_8051_set_clock: |
---|
| 567 | ∀M: Type[0]. |
---|
| 568 | ∀cm: M. |
---|
| 569 | ∀ps. |
---|
| 570 | ∀t. |
---|
| 571 | special_function_registers_8051 M cm (set_clock M cm ps t) = |
---|
| 572 | special_function_registers_8051 M cm ps. |
---|
| 573 | // |
---|
| 574 | qed. |
---|
| 575 | |
---|
| 576 | lemma get_arg_8_pseudo_addressing_mode_ok: |
---|
| 577 | ∀M: internal_pseudo_address_map. |
---|
| 578 | ∀cm: pseudo_assembly_program. |
---|
| 579 | ∀ps: PreStatus pseudo_assembly_program cm. |
---|
| 580 | ∀sigma: Word → Word. |
---|
| 581 | ∀policy: Word → bool. |
---|
| 582 | ∀addr1: [[registr; direct]]. |
---|
| 583 | addressing_mode_ok pseudo_assembly_program M cm ps addr1 = true → |
---|
| 584 | get_arg_8 (BitVectorTrie Byte 16) |
---|
| 585 | (code_memory_of_pseudo_assembly_program cm sigma policy) |
---|
| 586 | (status_of_pseudo_status M cm ps sigma policy) true addr1 = |
---|
| 587 | get_arg_8 pseudo_assembly_program cm ps true addr1. |
---|
| 588 | [2,3: /2 by is_in_subvector_is_in_supervector, subaddressing_modein, I/ ] |
---|
| 589 | #M #cm #ps #sigma #policy #addr1 |
---|
| 590 | @(subaddressing_mode_elim … addr1) #arg whd in ⊢ (? → ???%); |
---|
| 591 | [1: |
---|
| 592 | whd in ⊢ (??%? → ??%?); |
---|
| 593 | whd in match bit_address_of_register; normalize nodelta |
---|
| 594 | @pair_elim #un #ln #un_ln_refl |
---|
| 595 | lapply (refl_to_jmrefl ??? un_ln_refl) -un_ln_refl #un_ln_refl |
---|
| 596 | @(pair_replace ?????????? un_ln_refl) |
---|
| 597 | [1: |
---|
| 598 | whd in match get_8051_sfr; normalize nodelta |
---|
| 599 | whd in match sfr_8051_index; normalize nodelta |
---|
| 600 | @eq_f <get_index_v_special_function_registers_8051_not_acc_a |
---|
| 601 | try % #absurd destruct(absurd) |
---|
| 602 | |2: |
---|
| 603 | #assembly_mode_ok_refl |
---|
| 604 | >low_internal_ram_of_pseudo_internal_ram_miss |
---|
| 605 | [1: |
---|
| 606 | % |
---|
| 607 | |2: |
---|
| 608 | cases (assoc_list_exists ?????) in assembly_mode_ok_refl; normalize nodelta |
---|
| 609 | #absurd try % @sym_eq assumption |
---|
| 610 | ] |
---|
| 611 | ] |
---|
| 612 | |2: |
---|
| 613 | #addressing_mode_ok_refl whd in ⊢ (??%?); |
---|
| 614 | @pair_elim #nu #nl #nu_nl_refl normalize nodelta |
---|
| 615 | @pair_elim #ignore #three_bits #ignore_three_bits_refl normalize nodelta |
---|
| 616 | inversion (get_index_v bool ????) #get_index_v_refl normalize nodelta |
---|
| 617 | [1: |
---|
| 618 | whd in ⊢ (??%%); normalize nodelta |
---|
| 619 | cases (eqb ??) normalize nodelta [1: % ] |
---|
| 620 | cases (eqb ??) normalize nodelta [1: % ] |
---|
| 621 | cases (eqb ??) normalize nodelta [1: % ] |
---|
| 622 | cases (eqb ??) normalize nodelta [1: % ] |
---|
| 623 | cases (eqb ??) normalize nodelta [1: |
---|
| 624 | @get_8051_sfr_status_of_pseudo_status |
---|
| 625 | #absurd destruct(absurd) |
---|
| 626 | ] |
---|
| 627 | cases (eqb ??) normalize nodelta [1: |
---|
| 628 | @get_8051_sfr_status_of_pseudo_status |
---|
| 629 | #absurd destruct(absurd) |
---|
| 630 | ] |
---|
| 631 | cases (eqb ??) normalize nodelta [1: |
---|
| 632 | @get_8051_sfr_status_of_pseudo_status |
---|
| 633 | #absurd destruct(absurd) |
---|
| 634 | ] |
---|
| 635 | cases (eqb ??) normalize nodelta [1: |
---|
| 636 | @get_8051_sfr_status_of_pseudo_status |
---|
| 637 | #absurd destruct(absurd) |
---|
| 638 | ] |
---|
| 639 | cases (eqb ??) normalize nodelta [1: |
---|
| 640 | @get_8051_sfr_status_of_pseudo_status |
---|
| 641 | #absurd destruct(absurd) |
---|
| 642 | ] |
---|
| 643 | cases (eqb ??) normalize nodelta [1: % ] |
---|
| 644 | cases (eqb ??) normalize nodelta [1: % ] |
---|
| 645 | cases (eqb ??) normalize nodelta [1: % ] |
---|
| 646 | cases (eqb ??) normalize nodelta [1: % ] |
---|
| 647 | cases (eqb ??) normalize nodelta [1: % ] |
---|
| 648 | cases (eqb ??) normalize nodelta [1: |
---|
| 649 | @get_8051_sfr_status_of_pseudo_status |
---|
| 650 | #absurd destruct(absurd) |
---|
| 651 | ] |
---|
| 652 | cases (eqb ??) normalize nodelta [1: |
---|
| 653 | @get_8051_sfr_status_of_pseudo_status |
---|
| 654 | #absurd destruct(absurd) |
---|
| 655 | ] |
---|
| 656 | cases (eqb ??) normalize nodelta [1: |
---|
| 657 | @get_8051_sfr_status_of_pseudo_status |
---|
| 658 | #absurd destruct(absurd) |
---|
| 659 | ] |
---|
| 660 | cases (eqb ??) normalize nodelta [1: |
---|
| 661 | @get_8051_sfr_status_of_pseudo_status |
---|
| 662 | #absurd destruct(absurd) |
---|
| 663 | ] |
---|
| 664 | cases (eqb ??) normalize nodelta [1: |
---|
| 665 | @get_8051_sfr_status_of_pseudo_status |
---|
| 666 | #absurd destruct(absurd) |
---|
| 667 | ] |
---|
| 668 | cases (eqb ??) normalize nodelta [1: |
---|
| 669 | @get_8051_sfr_status_of_pseudo_status |
---|
| 670 | #absurd destruct(absurd) |
---|
| 671 | ] |
---|
| 672 | cases (eqb ??) normalize nodelta [1: |
---|
| 673 | @get_8051_sfr_status_of_pseudo_status |
---|
| 674 | #absurd destruct(absurd) |
---|
| 675 | ] |
---|
| 676 | cases (eqb ??) normalize nodelta [1: |
---|
| 677 | @get_8051_sfr_status_of_pseudo_status |
---|
| 678 | #absurd destruct(absurd) |
---|
| 679 | ] |
---|
| 680 | cases (eqb ??) normalize nodelta [1: |
---|
| 681 | @get_8051_sfr_status_of_pseudo_status |
---|
| 682 | #absurd destruct(absurd) |
---|
| 683 | ] |
---|
| 684 | cases (eqb ??) normalize nodelta [1: |
---|
| 685 | @get_8051_sfr_status_of_pseudo_status |
---|
| 686 | #absurd destruct(absurd) |
---|
| 687 | ] |
---|
| 688 | inversion (eqb ??) #eqb_refl normalize nodelta [1: |
---|
| 689 | @get_8051_sfr_status_of_pseudo_status lapply addressing_mode_ok_refl |
---|
| 690 | whd in ⊢ (??%? → ?); <(eqb_true_to_eq … eqb_refl) |
---|
| 691 | >bitvector_of_nat_inverse_nat_of_bitvector >eq_bv_refl normalize nodelta |
---|
| 692 | #assoc_list_assm cases (conjunction_true … assoc_list_assm) #_ |
---|
| 693 | #relevant #_ cases (eq_accumulator_address_map_entry_true_to_eq … relevant) % |
---|
| 694 | ] |
---|
| 695 | cases (eqb ??) normalize nodelta [1: |
---|
| 696 | @get_8051_sfr_status_of_pseudo_status |
---|
| 697 | #absurd destruct(absurd) |
---|
| 698 | ] % |
---|
| 699 | |2: |
---|
| 700 | lapply addressing_mode_ok_refl whd in ⊢ (??%? → ?); #relevant |
---|
| 701 | whd in match status_of_pseudo_status; normalize nodelta |
---|
| 702 | >low_internal_ram_of_pseudo_internal_ram_miss try % |
---|
| 703 | cut(arg = false:::(three_bits@@nl)) |
---|
| 704 | [1: |
---|
| 705 | <get_index_v_refl |
---|
| 706 | cut(nu=get_index_v bool 4 nu O (le_S_S O 3 (le_O_n 3)):::three_bits) |
---|
| 707 | [1: |
---|
| 708 | cut(ignore = [[get_index_v bool 4 nu 0 ?]]) |
---|
| 709 | [1: |
---|
| 710 | @le_S_S @le_O_n |
---|
| 711 | |2: |
---|
| 712 | cut(ignore = \fst (vsplit bool 1 3 nu)) |
---|
| 713 | [1: |
---|
| 714 | >ignore_three_bits_refl % |
---|
| 715 | |2: |
---|
| 716 | #ignore_refl >ignore_refl |
---|
| 717 | cases (bitvector_cases_hd_tl … nu) #hd * #tl #nu_refl |
---|
| 718 | >nu_refl % |
---|
| 719 | ] |
---|
| 720 | |3: |
---|
| 721 | #ignore_refl >ignore_refl in ignore_three_bits_refl; |
---|
| 722 | #relevant lapply (vsplit_ok ?????? (sym_eq … relevant)) |
---|
| 723 | #nu_refl <nu_refl % |
---|
| 724 | ] |
---|
| 725 | |2: |
---|
| 726 | #nu_refl change with (? = (?:::three_bits)@@?) <nu_refl |
---|
| 727 | @sym_eq @vsplit_ok >nu_nl_refl % |
---|
| 728 | ] |
---|
| 729 | |2: |
---|
| 730 | #arg_refl <arg_refl cases (assoc_list_exists ?????) in relevant; |
---|
| 731 | normalize nodelta |
---|
| 732 | [1: |
---|
| 733 | cases (eq_bv ???) normalize #absurd destruct(absurd) |
---|
| 734 | |2: |
---|
| 735 | #_ % |
---|
| 736 | ] |
---|
| 737 | ] |
---|
| 738 | ] |
---|
| 739 | ] |
---|
| 740 | qed. |
---|
| 741 | |
---|
| 742 | lemma special_function_registers_8051_set_program_counter: |
---|
| 743 | ∀M: Type[0]. |
---|
| 744 | ∀cm: M. |
---|
| 745 | ∀ps. |
---|
| 746 | ∀pc: Word. |
---|
| 747 | special_function_registers_8051 M cm (set_program_counter M cm ps pc) = |
---|
| 748 | special_function_registers_8051 M cm ps. |
---|
| 749 | // |
---|
| 750 | qed. |
---|
| 751 | |
---|
| 752 | lemma special_function_registers_8052_set_program_counter: |
---|
| 753 | ∀M: Type[0]. |
---|
| 754 | ∀cm: M. |
---|
| 755 | ∀ps. |
---|
| 756 | ∀pc: Word. |
---|
| 757 | special_function_registers_8052 M cm (set_program_counter M cm ps pc) = |
---|
| 758 | special_function_registers_8052 M cm ps. |
---|
| 759 | // |
---|
| 760 | qed. |
---|
| 761 | |
---|
| 762 | lemma set_index_set_index_commutation: |
---|
| 763 | ∀A: Type[0]. |
---|
| 764 | ∀n: nat. |
---|
| 765 | ∀v: Vector A n. |
---|
| 766 | ∀m, o: nat. |
---|
| 767 | ∀m_lt_proof: m < n. |
---|
| 768 | ∀o_lt_proof: o < n. |
---|
| 769 | ∀e, f: A. |
---|
| 770 | m ≠ o → |
---|
| 771 | set_index A n (set_index A n v o f o_lt_proof) m e m_lt_proof = |
---|
| 772 | set_index A n (set_index A n v m e m_lt_proof) o f o_lt_proof. |
---|
| 773 | #A #n #v elim v |
---|
| 774 | [1: |
---|
| 775 | #m #o #m_lt_proof |
---|
| 776 | normalize in m_lt_proof; cases (lt_to_not_zero … m_lt_proof) |
---|
| 777 | |2: |
---|
| 778 | #n' #hd #tl #inductive_hypothesis |
---|
| 779 | #m #o |
---|
| 780 | cases m cases o |
---|
| 781 | [1: |
---|
| 782 | #m_lt_proof #o_lt_proof #e #f #absurd @⊥ cases absurd #relevant |
---|
| 783 | @relevant % |
---|
| 784 | |2,3: |
---|
| 785 | #o' normalize // |
---|
| 786 | |4: |
---|
| 787 | #m' #o' #m_lt_proof #o_lt_proof #e #f #o_neq_m_assm |
---|
| 788 | normalize @eq_f @inductive_hypothesis @nmk #relevant |
---|
| 789 | >relevant in o_neq_m_assm; #relevant @(absurd ?? relevant) % |
---|
| 790 | ] |
---|
| 791 | ] |
---|
| 792 | qed. |
---|
| 793 | |
---|
| 794 | lemma special_function_registers_8051_sfr_8051_of_pseudo_sfr_8051: |
---|
| 795 | ∀M: internal_pseudo_address_map. |
---|
| 796 | ∀cm: pseudo_assembly_program. |
---|
| 797 | ∀ps. |
---|
| 798 | ∀sigma: Word → Word. |
---|
| 799 | ∀policy: Word → bool. |
---|
| 800 | ∀sfr. |
---|
| 801 | ∀result: Byte. |
---|
| 802 | eqb (sfr_8051_index sfr) (sfr_8051_index SFR_ACC_A) = false → |
---|
| 803 | special_function_registers_8051 (BitVectorTrie Byte 16) |
---|
| 804 | (code_memory_of_pseudo_assembly_program cm sigma policy) |
---|
| 805 | (set_8051_sfr (BitVectorTrie Byte 16) |
---|
| 806 | (code_memory_of_pseudo_assembly_program cm sigma policy) |
---|
| 807 | (status_of_pseudo_status M cm ps sigma policy) sfr result) = |
---|
| 808 | sfr_8051_of_pseudo_sfr_8051 M |
---|
| 809 | (special_function_registers_8051 pseudo_assembly_program cm |
---|
| 810 | (set_8051_sfr pseudo_assembly_program cm ps sfr result)) sigma. |
---|
| 811 | #M #cm #ps #sigma #policy #sfr #result #sfr_neq_assm |
---|
| 812 | whd in match (set_8051_sfr ?????); |
---|
| 813 | cases M #callM * try % #upper_lower #address |
---|
| 814 | whd in match (special_function_registers_8051 ???); |
---|
| 815 | whd in match (sfr_8051_of_pseudo_sfr_8051 ???); |
---|
| 816 | @pair_elim #high #low #high_low_refl normalize nodelta |
---|
| 817 | cases (eq_upper_lower ??) normalize nodelta |
---|
| 818 | whd in match (set_8051_sfr ?????); |
---|
| 819 | @set_index_set_index_commutation @nmk #relevant |
---|
| 820 | @(absurd ? relevant (eqb_false_to_not_eq ?? sfr_neq_assm)) |
---|
| 821 | qed. |
---|
| 822 | |
---|
| 823 | lemma special_function_registers_8051_set_arg_8: |
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| 824 | ∀M: internal_pseudo_address_map. |
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| 825 | ∀cm: pseudo_assembly_program. |
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| 826 | ∀ps. |
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| 827 | ∀sigma: Word → Word. |
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| 828 | ∀policy: Word → bool. |
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| 829 | ∀addr1: [[ registr; direct ]]. |
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| 830 | ∀result. |
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| 831 | addressing_mode_ok pseudo_assembly_program M cm ps addr1 = true → |
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| 832 | special_function_registers_8051 (BitVectorTrie Byte 16) |
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| 833 | (code_memory_of_pseudo_assembly_program cm sigma policy) |
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| 834 | (set_arg_8 (BitVectorTrie Byte 16) |
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| 835 | (code_memory_of_pseudo_assembly_program cm sigma policy) |
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| 836 | (status_of_pseudo_status M cm ps sigma policy) addr1 result) = |
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| 837 | sfr_8051_of_pseudo_sfr_8051 M |
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| 838 | (special_function_registers_8051 pseudo_assembly_program cm |
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| 839 | (set_arg_8 pseudo_assembly_program cm ps addr1 result)) sigma. |
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| 840 | cases daemon |
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| 841 | (* |
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| 842 | [2,3: /2 by is_in_subvector_is_in_supervector, subaddressing_modein, I/ ] |
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| 843 | #M #cm #ps #sigma #policy #addr1 #result |
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| 844 | @(subaddressing_mode_elim … addr1) #w #addressing_mode_ok_refl try % |
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| 845 | whd in match (set_arg_8 ?????); whd in ⊢ (??(???(???%))?); |
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| 846 | whd in match (set_arg_8 ?????) in ⊢ (???%); whd in ⊢ (???(??(???(???%))?)); |
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| 847 | cases (vsplit bool ???) #nu #nl normalize nodelta |
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| 848 | cases (vsplit bool ???) #ignore #three_bits normalize nodelta |
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| 849 | cases (get_index_v bool ????) normalize nodelta try % |
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| 850 | whd in match (set_bit_addressable_sfr ?????); whd in match (set_bit_addressable_sfr ?????) in ⊢ (???%); |
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| 851 | cases (eqb ??) normalize nodelta [1: cases not_implemented ] |
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| 852 | cases (eqb ??) normalize nodelta [1: % ] |
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| 853 | cases (eqb ??) normalize nodelta [1: cases not_implemented ] |
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| 854 | cases (eqb ??) normalize nodelta [1: % ] |
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| 855 | cases (eqb ??) normalize nodelta [1: @special_function_registers_8051_sfr_8051_of_pseudo_sfr_8051 % ] |
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| 856 | cases (eqb ??) normalize nodelta [1: @special_function_registers_8051_sfr_8051_of_pseudo_sfr_8051 % ] |
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| 857 | cases (eqb ??) normalize nodelta [1: @special_function_registers_8051_sfr_8051_of_pseudo_sfr_8051 % ] |
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| 858 | cases (eqb ??) normalize nodelta [1: @special_function_registers_8051_sfr_8051_of_pseudo_sfr_8051 % ] |
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| 859 | cases (eqb ??) normalize nodelta [1: @special_function_registers_8051_sfr_8051_of_pseudo_sfr_8051 % ] |
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| 860 | cases (eqb ??) normalize nodelta [1: % ] |
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| 861 | cases (eqb ??) normalize nodelta [1: % ] |
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| 862 | cases (eqb ??) normalize nodelta [1: % ] |
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| 863 | cases (eqb ??) normalize nodelta [1: % ] |
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| 864 | cases (eqb ??) normalize nodelta [1: % ] |
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| 865 | cases (eqb ??) normalize nodelta [1: @special_function_registers_8051_sfr_8051_of_pseudo_sfr_8051 % ] |
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| 866 | cases (eqb ??) normalize nodelta [1: @special_function_registers_8051_sfr_8051_of_pseudo_sfr_8051 % ] |
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| 867 | cases (eqb ??) normalize nodelta [1: @special_function_registers_8051_sfr_8051_of_pseudo_sfr_8051 % ] |
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| 868 | cases (eqb ??) normalize nodelta [1: @special_function_registers_8051_sfr_8051_of_pseudo_sfr_8051 % ] |
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| 869 | cases (eqb ??) normalize nodelta [1: @special_function_registers_8051_sfr_8051_of_pseudo_sfr_8051 % ] |
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| 870 | cases (eqb ??) normalize nodelta [1: @special_function_registers_8051_sfr_8051_of_pseudo_sfr_8051 % ] |
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| 871 | cases (eqb ??) normalize nodelta [1: @special_function_registers_8051_sfr_8051_of_pseudo_sfr_8051 % ] |
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| 872 | cases (eqb ??) normalize nodelta [1: @special_function_registers_8051_sfr_8051_of_pseudo_sfr_8051 % ] |
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| 873 | cases (eqb ??) normalize nodelta [1: @special_function_registers_8051_sfr_8051_of_pseudo_sfr_8051 % ] |
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| 874 | cases (eqb ??) normalize nodelta [1: @special_function_registers_8051_sfr_8051_of_pseudo_sfr_8051 % ] |
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| 875 | inversion (eqb ??) #eqb_refl normalize nodelta [1: |
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| 876 | whd in addressing_mode_ok_refl:(??%?); <(eqb_true_to_eq … eqb_refl) in addressing_mode_ok_refl; |
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| 877 | >bitvector_of_nat_inverse_nat_of_bitvector >eq_bv_refl normalize nodelta |
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| 878 | #relevant cases (conjunction_true … relevant) #_ #eq_acc_assm |
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| 879 | whd in match (status_of_pseudo_status ?????); |
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| 880 | whd in match sfr_8051_of_pseudo_sfr_8051; normalize nodelta |
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| 881 | >(eq_accumulator_address_map_entry_true_to_eq … eq_acc_assm) normalize nodelta % |
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| 882 | ] |
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| 883 | cases (eqb ??) normalize nodelta [1: @special_function_registers_8051_sfr_8051_of_pseudo_sfr_8051 % ] |
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| 884 | cases not_implemented *) |
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| 885 | qed. |
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