Changeset 1062 for src/ASM/FoldStuff.ma
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 Jul 11, 2011, 2:09:03 PM (9 years ago)
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src/ASM/FoldStuff.ma
r1014 r1062 1 (* RUSSEL **)2 3 include "basics/jmeq.ma".4 include "basics/types.ma".5 include "basics/list.ma".6 7 notation > "hvbox(a break ≃ b)"8 non associative with precedence 459 for @{ 'jmeq ? $a ? $b }.10 11 notation < "hvbox(term 46 a break maction (≃) (≃\sub(t,u)) term 46 b)"12 non associative with precedence 4513 for @{ 'jmeq $t $a $u $b }.14 15 interpretation "john major's equality" 'jmeq t x u y = (jmeq t x u y).16 17 lemma eq_to_jmeq:18 ∀A: Type[0].19 ∀x, y: A.20 x = y → x ≃ y.21 //22 qed.23 24 definition inject : ∀A.∀P:A → Prop.∀a.∀p:P a.Σx:A.P x ≝ λA,P,a,p. dp … a p.25 definition eject : ∀A.∀P: A → Prop.(Σx:A.P x) → A ≝ λA,P,c.match c with [ dp w p ⇒ w].26 27 coercion inject nocomposites: ∀A.∀P:A → Prop.∀a.∀p:P a.Σx:A.P x ≝ inject on a:? to Σx:?.?.28 coercion eject nocomposites: ∀A.∀P:A → Prop.∀c:Σx:A.P x.A ≝ eject on _c:Σx:?.? to ?.29 30 (*axiom VOID: Type[0].31 axiom assert_false: VOID.32 definition bigbang: ∀A:Type[0].False → VOID → A.33 #A #abs cases abs34 qed.35 36 coercion bigbang nocomposites: ∀A:Type[0].False → ∀v:VOID.A ≝ bigbang on _v:VOID to ?.*)37 38 lemma sig2: ∀A.∀P:A → Prop. ∀p:Σx:A.P x. P (eject … p).39 #A #P #p cases p #w #q @q40 qed.41 42 lemma jmeq_to_eq: ∀A:Type[0]. ∀x,y:A. x≃y → x=y.43 #A #x #y #JMEQ @(jmeq_elim ? x … JMEQ) %44 qed.45 46 coercion jmeq_to_eq: ∀A:Type[0]. ∀x,y:A. ∀p:x≃y.x=y ≝ jmeq_to_eq on _p:?≃? to ?=?.47 48 (* END RUSSELL **)49 50 1 include "ASM/Util.ma". 2 include "ASM/JMCoercions.ma". 51 3 52 4 let rec foldl_strong_internal
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