[2601] | 1 | open Preamble |
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| 2 | |
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| 3 | open Hints_declaration |
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| 4 | |
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| 5 | open Core_notation |
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| 6 | |
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| 7 | open Pts |
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| 8 | |
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| 9 | open Logic |
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| 10 | |
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| 11 | open Bool |
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| 12 | |
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| 13 | open Relations |
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| 14 | |
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| 15 | open Nat |
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| 16 | |
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| 17 | type compare = |
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| 18 | | LT |
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| 19 | | EQ |
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| 20 | | GT |
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| 21 | |
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| 22 | (** val compare_rect_Type4 : 'a1 -> 'a1 -> 'a1 -> compare -> 'a1 **) |
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| 23 | let rec compare_rect_Type4 h_LT h_EQ h_GT = function |
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| 24 | | LT -> h_LT |
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| 25 | | EQ -> h_EQ |
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| 26 | | GT -> h_GT |
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| 27 | |
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| 28 | (** val compare_rect_Type5 : 'a1 -> 'a1 -> 'a1 -> compare -> 'a1 **) |
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| 29 | let rec compare_rect_Type5 h_LT h_EQ h_GT = function |
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| 30 | | LT -> h_LT |
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| 31 | | EQ -> h_EQ |
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| 32 | | GT -> h_GT |
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| 33 | |
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| 34 | (** val compare_rect_Type3 : 'a1 -> 'a1 -> 'a1 -> compare -> 'a1 **) |
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| 35 | let rec compare_rect_Type3 h_LT h_EQ h_GT = function |
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| 36 | | LT -> h_LT |
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| 37 | | EQ -> h_EQ |
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| 38 | | GT -> h_GT |
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| 39 | |
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| 40 | (** val compare_rect_Type2 : 'a1 -> 'a1 -> 'a1 -> compare -> 'a1 **) |
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| 41 | let rec compare_rect_Type2 h_LT h_EQ h_GT = function |
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| 42 | | LT -> h_LT |
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| 43 | | EQ -> h_EQ |
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| 44 | | GT -> h_GT |
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| 45 | |
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| 46 | (** val compare_rect_Type1 : 'a1 -> 'a1 -> 'a1 -> compare -> 'a1 **) |
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| 47 | let rec compare_rect_Type1 h_LT h_EQ h_GT = function |
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| 48 | | LT -> h_LT |
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| 49 | | EQ -> h_EQ |
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| 50 | | GT -> h_GT |
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| 51 | |
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| 52 | (** val compare_rect_Type0 : 'a1 -> 'a1 -> 'a1 -> compare -> 'a1 **) |
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| 53 | let rec compare_rect_Type0 h_LT h_EQ h_GT = function |
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| 54 | | LT -> h_LT |
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| 55 | | EQ -> h_EQ |
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| 56 | | GT -> h_GT |
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| 57 | |
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| 58 | (** val compare_inv_rect_Type4 : |
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| 59 | compare -> (__ -> 'a1) -> (__ -> 'a1) -> (__ -> 'a1) -> 'a1 **) |
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| 60 | let compare_inv_rect_Type4 hterm h1 h2 h3 = |
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| 61 | let hcut = compare_rect_Type4 h1 h2 h3 hterm in hcut __ |
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| 62 | |
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| 63 | (** val compare_inv_rect_Type3 : |
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| 64 | compare -> (__ -> 'a1) -> (__ -> 'a1) -> (__ -> 'a1) -> 'a1 **) |
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| 65 | let compare_inv_rect_Type3 hterm h1 h2 h3 = |
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| 66 | let hcut = compare_rect_Type3 h1 h2 h3 hterm in hcut __ |
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| 67 | |
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| 68 | (** val compare_inv_rect_Type2 : |
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| 69 | compare -> (__ -> 'a1) -> (__ -> 'a1) -> (__ -> 'a1) -> 'a1 **) |
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| 70 | let compare_inv_rect_Type2 hterm h1 h2 h3 = |
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| 71 | let hcut = compare_rect_Type2 h1 h2 h3 hterm in hcut __ |
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| 72 | |
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| 73 | (** val compare_inv_rect_Type1 : |
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| 74 | compare -> (__ -> 'a1) -> (__ -> 'a1) -> (__ -> 'a1) -> 'a1 **) |
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| 75 | let compare_inv_rect_Type1 hterm h1 h2 h3 = |
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| 76 | let hcut = compare_rect_Type1 h1 h2 h3 hterm in hcut __ |
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| 77 | |
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| 78 | (** val compare_inv_rect_Type0 : |
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| 79 | compare -> (__ -> 'a1) -> (__ -> 'a1) -> (__ -> 'a1) -> 'a1 **) |
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| 80 | let compare_inv_rect_Type0 hterm h1 h2 h3 = |
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| 81 | let hcut = compare_rect_Type0 h1 h2 h3 hterm in hcut __ |
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| 82 | |
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| 83 | (** val compare_discr : compare -> compare -> __ **) |
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| 84 | let compare_discr x y = |
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| 85 | Logic.eq_rect_Type2 x |
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| 86 | (match x with |
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| 87 | | LT -> Obj.magic (fun _ dH -> dH) |
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| 88 | | EQ -> Obj.magic (fun _ dH -> dH) |
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| 89 | | GT -> Obj.magic (fun _ dH -> dH)) y |
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| 90 | |
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| 91 | (** val compare_invert : compare -> compare **) |
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| 92 | let compare_invert = function |
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| 93 | | LT -> GT |
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| 94 | | EQ -> EQ |
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| 95 | | GT -> LT |
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| 96 | |
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| 97 | type pos = |
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| 98 | | One |
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| 99 | | P1 of pos |
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| 100 | | P0 of pos |
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| 101 | |
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| 102 | (** val pos_rect_Type4 : |
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| 103 | 'a1 -> (pos -> 'a1 -> 'a1) -> (pos -> 'a1 -> 'a1) -> pos -> 'a1 **) |
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| 104 | let rec pos_rect_Type4 h_one h_p1 h_p0 = function |
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| 105 | | One -> h_one |
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[2775] | 106 | | P1 x_1606 -> h_p1 x_1606 (pos_rect_Type4 h_one h_p1 h_p0 x_1606) |
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| 107 | | P0 x_1607 -> h_p0 x_1607 (pos_rect_Type4 h_one h_p1 h_p0 x_1607) |
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[2601] | 108 | |
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| 109 | (** val pos_rect_Type3 : |
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| 110 | 'a1 -> (pos -> 'a1 -> 'a1) -> (pos -> 'a1 -> 'a1) -> pos -> 'a1 **) |
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| 111 | let rec pos_rect_Type3 h_one h_p1 h_p0 = function |
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| 112 | | One -> h_one |
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[2775] | 113 | | P1 x_1618 -> h_p1 x_1618 (pos_rect_Type3 h_one h_p1 h_p0 x_1618) |
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| 114 | | P0 x_1619 -> h_p0 x_1619 (pos_rect_Type3 h_one h_p1 h_p0 x_1619) |
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[2601] | 115 | |
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| 116 | (** val pos_rect_Type2 : |
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| 117 | 'a1 -> (pos -> 'a1 -> 'a1) -> (pos -> 'a1 -> 'a1) -> pos -> 'a1 **) |
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| 118 | let rec pos_rect_Type2 h_one h_p1 h_p0 = function |
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| 119 | | One -> h_one |
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[2775] | 120 | | P1 x_1624 -> h_p1 x_1624 (pos_rect_Type2 h_one h_p1 h_p0 x_1624) |
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| 121 | | P0 x_1625 -> h_p0 x_1625 (pos_rect_Type2 h_one h_p1 h_p0 x_1625) |
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[2601] | 122 | |
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| 123 | (** val pos_rect_Type1 : |
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| 124 | 'a1 -> (pos -> 'a1 -> 'a1) -> (pos -> 'a1 -> 'a1) -> pos -> 'a1 **) |
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| 125 | let rec pos_rect_Type1 h_one h_p1 h_p0 = function |
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| 126 | | One -> h_one |
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[2775] | 127 | | P1 x_1630 -> h_p1 x_1630 (pos_rect_Type1 h_one h_p1 h_p0 x_1630) |
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| 128 | | P0 x_1631 -> h_p0 x_1631 (pos_rect_Type1 h_one h_p1 h_p0 x_1631) |
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[2601] | 129 | |
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| 130 | (** val pos_rect_Type0 : |
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| 131 | 'a1 -> (pos -> 'a1 -> 'a1) -> (pos -> 'a1 -> 'a1) -> pos -> 'a1 **) |
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| 132 | let rec pos_rect_Type0 h_one h_p1 h_p0 = function |
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| 133 | | One -> h_one |
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[2775] | 134 | | P1 x_1636 -> h_p1 x_1636 (pos_rect_Type0 h_one h_p1 h_p0 x_1636) |
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| 135 | | P0 x_1637 -> h_p0 x_1637 (pos_rect_Type0 h_one h_p1 h_p0 x_1637) |
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[2601] | 136 | |
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| 137 | (** val pos_inv_rect_Type4 : |
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| 138 | pos -> (__ -> 'a1) -> (pos -> (__ -> 'a1) -> __ -> 'a1) -> (pos -> (__ -> |
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| 139 | 'a1) -> __ -> 'a1) -> 'a1 **) |
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| 140 | let pos_inv_rect_Type4 hterm h1 h2 h3 = |
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| 141 | let hcut = pos_rect_Type4 h1 h2 h3 hterm in hcut __ |
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| 142 | |
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| 143 | (** val pos_inv_rect_Type3 : |
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| 144 | pos -> (__ -> 'a1) -> (pos -> (__ -> 'a1) -> __ -> 'a1) -> (pos -> (__ -> |
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| 145 | 'a1) -> __ -> 'a1) -> 'a1 **) |
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| 146 | let pos_inv_rect_Type3 hterm h1 h2 h3 = |
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| 147 | let hcut = pos_rect_Type3 h1 h2 h3 hterm in hcut __ |
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| 148 | |
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| 149 | (** val pos_inv_rect_Type2 : |
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| 150 | pos -> (__ -> 'a1) -> (pos -> (__ -> 'a1) -> __ -> 'a1) -> (pos -> (__ -> |
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| 151 | 'a1) -> __ -> 'a1) -> 'a1 **) |
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| 152 | let pos_inv_rect_Type2 hterm h1 h2 h3 = |
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| 153 | let hcut = pos_rect_Type2 h1 h2 h3 hterm in hcut __ |
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| 154 | |
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| 155 | (** val pos_inv_rect_Type1 : |
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| 156 | pos -> (__ -> 'a1) -> (pos -> (__ -> 'a1) -> __ -> 'a1) -> (pos -> (__ -> |
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| 157 | 'a1) -> __ -> 'a1) -> 'a1 **) |
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| 158 | let pos_inv_rect_Type1 hterm h1 h2 h3 = |
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| 159 | let hcut = pos_rect_Type1 h1 h2 h3 hterm in hcut __ |
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| 160 | |
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| 161 | (** val pos_inv_rect_Type0 : |
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| 162 | pos -> (__ -> 'a1) -> (pos -> (__ -> 'a1) -> __ -> 'a1) -> (pos -> (__ -> |
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| 163 | 'a1) -> __ -> 'a1) -> 'a1 **) |
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| 164 | let pos_inv_rect_Type0 hterm h1 h2 h3 = |
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| 165 | let hcut = pos_rect_Type0 h1 h2 h3 hterm in hcut __ |
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| 166 | |
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| 167 | (** val pos_discr : pos -> pos -> __ **) |
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| 168 | let pos_discr x y = |
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| 169 | Logic.eq_rect_Type2 x |
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| 170 | (match x with |
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| 171 | | One -> Obj.magic (fun _ dH -> dH) |
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| 172 | | P1 a0 -> Obj.magic (fun _ dH -> dH __) |
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| 173 | | P0 a0 -> Obj.magic (fun _ dH -> dH __)) y |
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| 174 | |
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[2773] | 175 | (** val pred : pos -> pos **) |
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| 176 | let rec pred = function |
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[2601] | 177 | | One -> One |
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| 178 | | P1 ps -> P0 ps |
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| 179 | | P0 ps -> |
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| 180 | (match ps with |
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| 181 | | One -> One |
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[2773] | 182 | | P1 x -> P1 (pred ps) |
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| 183 | | P0 x -> P1 (pred ps)) |
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[2601] | 184 | |
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| 185 | (** val succ : pos -> pos **) |
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| 186 | let rec succ = function |
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| 187 | | One -> P0 One |
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| 188 | | P1 ps -> P0 (succ ps) |
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| 189 | | P0 ps -> P1 ps |
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| 190 | |
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| 191 | (** val nat_of_pos : pos -> Nat.nat **) |
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| 192 | let rec nat_of_pos = function |
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| 193 | | One -> Nat.S Nat.O |
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| 194 | | P1 ps -> Nat.S (Nat.times (Nat.S (Nat.S Nat.O)) (nat_of_pos ps)) |
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| 195 | | P0 ps -> Nat.times (Nat.S (Nat.S Nat.O)) (nat_of_pos ps) |
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| 196 | |
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| 197 | (** val succ_pos_of_nat : Nat.nat -> pos **) |
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| 198 | let rec succ_pos_of_nat = function |
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| 199 | | Nat.O -> One |
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| 200 | | Nat.S n' -> succ (succ_pos_of_nat n') |
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| 201 | |
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[2773] | 202 | (** val plus : pos -> pos -> pos **) |
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| 203 | let rec plus n m = |
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[2601] | 204 | match n with |
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| 205 | | One -> succ m |
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| 206 | | P1 n' -> |
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| 207 | (match m with |
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| 208 | | One -> succ n |
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[2773] | 209 | | P1 m' -> P0 (succ (plus n' m')) |
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| 210 | | P0 m' -> P1 (plus n' m')) |
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[2601] | 211 | | P0 n' -> |
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| 212 | (match m with |
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| 213 | | One -> P1 n' |
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[2773] | 214 | | P1 m' -> P1 (plus n' m') |
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| 215 | | P0 m' -> P0 (plus n' m')) |
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[2601] | 216 | |
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[2773] | 217 | (** val times : pos -> pos -> pos **) |
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| 218 | let rec times n m = |
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[2601] | 219 | match n with |
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| 220 | | One -> m |
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[2773] | 221 | | P1 n' -> plus m (P0 (times n' m)) |
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| 222 | | P0 n' -> P0 (times n' m) |
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[2601] | 223 | |
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| 224 | type minusresult = |
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| 225 | | MinusNeg |
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| 226 | | MinusZero |
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| 227 | | MinusPos of pos |
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| 228 | |
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| 229 | (** val minusresult_rect_Type4 : |
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| 230 | 'a1 -> 'a1 -> (pos -> 'a1) -> minusresult -> 'a1 **) |
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| 231 | let rec minusresult_rect_Type4 h_MinusNeg h_MinusZero h_MinusPos = function |
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| 232 | | MinusNeg -> h_MinusNeg |
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| 233 | | MinusZero -> h_MinusZero |
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[2775] | 234 | | MinusPos x_1813 -> h_MinusPos x_1813 |
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[2601] | 235 | |
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| 236 | (** val minusresult_rect_Type5 : |
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| 237 | 'a1 -> 'a1 -> (pos -> 'a1) -> minusresult -> 'a1 **) |
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| 238 | let rec minusresult_rect_Type5 h_MinusNeg h_MinusZero h_MinusPos = function |
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| 239 | | MinusNeg -> h_MinusNeg |
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| 240 | | MinusZero -> h_MinusZero |
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[2775] | 241 | | MinusPos x_1818 -> h_MinusPos x_1818 |
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[2601] | 242 | |
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| 243 | (** val minusresult_rect_Type3 : |
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| 244 | 'a1 -> 'a1 -> (pos -> 'a1) -> minusresult -> 'a1 **) |
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| 245 | let rec minusresult_rect_Type3 h_MinusNeg h_MinusZero h_MinusPos = function |
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| 246 | | MinusNeg -> h_MinusNeg |
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| 247 | | MinusZero -> h_MinusZero |
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[2775] | 248 | | MinusPos x_1823 -> h_MinusPos x_1823 |
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[2601] | 249 | |
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| 250 | (** val minusresult_rect_Type2 : |
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| 251 | 'a1 -> 'a1 -> (pos -> 'a1) -> minusresult -> 'a1 **) |
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| 252 | let rec minusresult_rect_Type2 h_MinusNeg h_MinusZero h_MinusPos = function |
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| 253 | | MinusNeg -> h_MinusNeg |
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| 254 | | MinusZero -> h_MinusZero |
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[2775] | 255 | | MinusPos x_1828 -> h_MinusPos x_1828 |
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[2601] | 256 | |
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| 257 | (** val minusresult_rect_Type1 : |
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| 258 | 'a1 -> 'a1 -> (pos -> 'a1) -> minusresult -> 'a1 **) |
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| 259 | let rec minusresult_rect_Type1 h_MinusNeg h_MinusZero h_MinusPos = function |
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| 260 | | MinusNeg -> h_MinusNeg |
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| 261 | | MinusZero -> h_MinusZero |
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[2775] | 262 | | MinusPos x_1833 -> h_MinusPos x_1833 |
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[2601] | 263 | |
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| 264 | (** val minusresult_rect_Type0 : |
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| 265 | 'a1 -> 'a1 -> (pos -> 'a1) -> minusresult -> 'a1 **) |
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| 266 | let rec minusresult_rect_Type0 h_MinusNeg h_MinusZero h_MinusPos = function |
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| 267 | | MinusNeg -> h_MinusNeg |
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| 268 | | MinusZero -> h_MinusZero |
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[2775] | 269 | | MinusPos x_1838 -> h_MinusPos x_1838 |
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[2601] | 270 | |
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| 271 | (** val minusresult_inv_rect_Type4 : |
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| 272 | minusresult -> (__ -> 'a1) -> (__ -> 'a1) -> (pos -> __ -> 'a1) -> 'a1 **) |
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| 273 | let minusresult_inv_rect_Type4 hterm h1 h2 h3 = |
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| 274 | let hcut = minusresult_rect_Type4 h1 h2 h3 hterm in hcut __ |
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| 275 | |
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| 276 | (** val minusresult_inv_rect_Type3 : |
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| 277 | minusresult -> (__ -> 'a1) -> (__ -> 'a1) -> (pos -> __ -> 'a1) -> 'a1 **) |
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| 278 | let minusresult_inv_rect_Type3 hterm h1 h2 h3 = |
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| 279 | let hcut = minusresult_rect_Type3 h1 h2 h3 hterm in hcut __ |
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| 280 | |
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| 281 | (** val minusresult_inv_rect_Type2 : |
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| 282 | minusresult -> (__ -> 'a1) -> (__ -> 'a1) -> (pos -> __ -> 'a1) -> 'a1 **) |
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| 283 | let minusresult_inv_rect_Type2 hterm h1 h2 h3 = |
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| 284 | let hcut = minusresult_rect_Type2 h1 h2 h3 hterm in hcut __ |
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| 285 | |
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| 286 | (** val minusresult_inv_rect_Type1 : |
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| 287 | minusresult -> (__ -> 'a1) -> (__ -> 'a1) -> (pos -> __ -> 'a1) -> 'a1 **) |
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| 288 | let minusresult_inv_rect_Type1 hterm h1 h2 h3 = |
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| 289 | let hcut = minusresult_rect_Type1 h1 h2 h3 hterm in hcut __ |
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| 290 | |
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| 291 | (** val minusresult_inv_rect_Type0 : |
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| 292 | minusresult -> (__ -> 'a1) -> (__ -> 'a1) -> (pos -> __ -> 'a1) -> 'a1 **) |
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| 293 | let minusresult_inv_rect_Type0 hterm h1 h2 h3 = |
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| 294 | let hcut = minusresult_rect_Type0 h1 h2 h3 hterm in hcut __ |
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| 295 | |
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| 296 | (** val minusresult_discr : minusresult -> minusresult -> __ **) |
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| 297 | let minusresult_discr x y = |
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| 298 | Logic.eq_rect_Type2 x |
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| 299 | (match x with |
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| 300 | | MinusNeg -> Obj.magic (fun _ dH -> dH) |
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| 301 | | MinusZero -> Obj.magic (fun _ dH -> dH) |
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| 302 | | MinusPos a0 -> Obj.magic (fun _ dH -> dH __)) y |
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| 303 | |
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| 304 | (** val partial_minus : pos -> pos -> minusresult **) |
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| 305 | let rec partial_minus n m = |
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| 306 | match n with |
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| 307 | | One -> |
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| 308 | (match m with |
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| 309 | | One -> MinusZero |
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| 310 | | P1 x -> MinusNeg |
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| 311 | | P0 x -> MinusNeg) |
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| 312 | | P1 n' -> |
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| 313 | (match m with |
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| 314 | | One -> MinusPos (P0 n') |
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| 315 | | P1 m' -> |
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| 316 | (match partial_minus n' m' with |
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| 317 | | MinusNeg -> MinusNeg |
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| 318 | | MinusZero -> MinusZero |
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| 319 | | MinusPos p -> MinusPos (P0 p)) |
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| 320 | | P0 m' -> |
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| 321 | (match partial_minus n' m' with |
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| 322 | | MinusNeg -> MinusNeg |
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| 323 | | MinusZero -> MinusPos One |
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| 324 | | MinusPos p -> MinusPos (P1 p))) |
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| 325 | | P0 n' -> |
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| 326 | (match m with |
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[2773] | 327 | | One -> MinusPos (pred n) |
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[2601] | 328 | | P1 m' -> |
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| 329 | (match partial_minus n' m' with |
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| 330 | | MinusNeg -> MinusNeg |
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| 331 | | MinusZero -> MinusNeg |
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[2773] | 332 | | MinusPos p -> MinusPos (pred (P0 p))) |
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[2601] | 333 | | P0 m' -> |
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| 334 | (match partial_minus n' m' with |
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| 335 | | MinusNeg -> MinusNeg |
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| 336 | | MinusZero -> MinusZero |
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| 337 | | MinusPos p -> MinusPos (P0 p))) |
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| 338 | |
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[2773] | 339 | (** val minus : pos -> pos -> pos **) |
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| 340 | let minus n m = |
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[2601] | 341 | match partial_minus n m with |
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| 342 | | MinusNeg -> One |
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| 343 | | MinusZero -> One |
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| 344 | | MinusPos p -> p |
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| 345 | |
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[2773] | 346 | (** val eqb : pos -> pos -> Bool.bool **) |
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| 347 | let rec eqb n m = |
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[2601] | 348 | match n with |
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| 349 | | One -> |
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| 350 | (match m with |
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| 351 | | One -> Bool.True |
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| 352 | | P1 x -> Bool.False |
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| 353 | | P0 x -> Bool.False) |
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| 354 | | P1 p -> |
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| 355 | (match m with |
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| 356 | | One -> Bool.False |
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[2773] | 357 | | P1 q -> eqb p q |
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[2601] | 358 | | P0 x -> Bool.False) |
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| 359 | | P0 p -> |
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| 360 | (match m with |
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| 361 | | One -> Bool.False |
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| 362 | | P1 x -> Bool.False |
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[2773] | 363 | | P0 q -> eqb p q) |
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[2601] | 364 | |
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| 365 | (** val eqb_elim : pos -> pos -> (__ -> 'a1) -> (__ -> 'a1) -> 'a1 **) |
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| 366 | let eqb_elim n m x x0 = |
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| 367 | pos_rect_Type1 (fun m0 -> |
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| 368 | match m0 with |
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| 369 | | One -> (fun _ auto auto' -> auto __) |
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| 370 | | P1 m' -> (fun _ t f -> f __) |
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| 371 | | P0 m' -> (fun _ t f -> f __)) (fun n' iH m0 -> |
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| 372 | match m0 with |
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| 373 | | One -> (fun _ t f -> f __) |
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| 374 | | P1 m' -> (fun _ t f -> iH m' __ (fun _ -> t __) (fun _ -> f __)) |
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| 375 | | P0 m' -> (fun _ t f -> f __)) (fun n' iH m0 -> |
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| 376 | match m0 with |
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| 377 | | One -> (fun _ t f -> f __) |
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| 378 | | P1 m' -> (fun _ t f -> f __) |
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| 379 | | P0 m' -> (fun _ t f -> iH m' __ (fun _ -> t __) (fun _ -> f __))) n m |
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| 380 | __ x x0 |
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| 381 | |
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[2773] | 382 | (** val leb : pos -> pos -> Bool.bool **) |
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| 383 | let rec leb n m = |
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[2601] | 384 | match partial_minus n m with |
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| 385 | | MinusNeg -> Bool.True |
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| 386 | | MinusZero -> Bool.True |
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| 387 | | MinusPos x -> Bool.False |
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| 388 | |
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| 389 | (** val pos_compare : pos -> pos -> compare **) |
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| 390 | let pos_compare n m = |
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| 391 | match partial_minus n m with |
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| 392 | | MinusNeg -> LT |
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| 393 | | MinusZero -> EQ |
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| 394 | | MinusPos x -> GT |
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| 395 | |
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| 396 | (** val two_power_nat : Nat.nat -> pos **) |
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| 397 | let rec two_power_nat = function |
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| 398 | | Nat.O -> One |
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| 399 | | Nat.S n' -> P0 (two_power_nat n') |
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| 400 | |
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| 401 | (** val two_power_pos : pos -> pos **) |
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| 402 | let two_power_pos p = |
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| 403 | two_power_nat (nat_of_pos p) |
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| 404 | |
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[2773] | 405 | (** val max : pos -> pos -> pos **) |
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| 406 | let max n m = |
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| 407 | match leb n m with |
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[2601] | 408 | | Bool.True -> m |
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| 409 | | Bool.False -> n |
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| 410 | |
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