source: Deliverables/D3.3/id-lookup-branch/ASM/JMCoercions.ma @ 3033

Last change on this file since 3033 was 1062, checked in by mulligan, 8 years ago

separated jmeq and coercions from foldstuff.ma in order to fix the ongoing mess in util.ma surrounding reduce_strong

File size: 1.4 KB
Line 
1include "basics/jmeq.ma".
2include "basics/types.ma".
3include "basics/list.ma".
4
5notation > "hvbox(a break ≃ b)"
6  non associative with precedence 45
7for @{ 'jmeq ? $a ? $b }.
8
9notation < "hvbox(term 46 a break maction (≃) (≃\sub(t,u)) term 46 b)"
10  non associative with precedence 45
11for @{ 'jmeq $t $a $u $b }.
12
13interpretation "john major's equality" 'jmeq t x u y = (jmeq t x u y).
14
15lemma eq_to_jmeq:
16  ∀A: Type[0].
17  ∀x, y: A.
18    x = y → x ≃ y.
19  //
20qed.
21
22definition inject : ∀A.∀P:A → Prop.∀a.∀p:P a.Σx:A.P x ≝ λA,P,a,p. dp … a p.
23definition eject : ∀A.∀P: A → Prop.(Σx:A.P x) → A ≝ λA,P,c.match c with [ dp w p ⇒ w].
24
25coercion inject nocomposites: ∀A.∀P:A → Prop.∀a.∀p:P a.Σx:A.P x ≝ inject on a:? to Σx:?.?.
26coercion eject nocomposites: ∀A.∀P:A → Prop.∀c:Σx:A.P x.A ≝ eject on _c:Σx:?.? to ?.
27
28(*axiom VOID: Type[0].
29axiom assert_false: VOID.
30definition bigbang: ∀A:Type[0].False → VOID → A.
31 #A #abs cases abs
32qed.
33
34coercion bigbang nocomposites: ∀A:Type[0].False → ∀v:VOID.A ≝ bigbang on _v:VOID to ?.*)
35
36lemma sig2: ∀A.∀P:A → Prop. ∀p:Σx:A.P x. P (eject … p).
37 #A #P #p cases p #w #q @q
38qed.
39
40lemma jmeq_to_eq: ∀A:Type[0]. ∀x,y:A. x≃y → x=y.
41 #A #x #y #JMEQ @(jmeq_elim ? x … JMEQ) %
42qed.
43
44coercion jmeq_to_eq: ∀A:Type[0]. ∀x,y:A. ∀p:x≃y.x=y ≝ jmeq_to_eq on _p:?≃? to ?=?.
45
46(* END RUSSELL **)
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