source: src/ASM/JMCoercions.ma @ 1599

Last change on this file since 1599 was 1599, checked in by sacerdot, 8 years ago

Start of merging of stuff into the standard library of Matita.

File size: 829 bytes
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1include "basics/jmeq.ma".
2include "basics/types.ma".
3include "basics/lists/list.ma".
4
5definition inject : ∀A.∀P:A → Prop.∀a.∀p:P a.Σx:A.P x ≝ λA,P,a,p. dp … a p.
6definition eject : ∀A.∀P: A → Prop.(Σx:A.P x) → A ≝ λA,P,c.match c with [ dp w p ⇒ w].
7
8coercion inject nocomposites: ∀A.∀P:A → Prop.∀a.∀p:P a.Σx:A.P x ≝ inject on a:? to Σx:?.?.
9coercion eject nocomposites: ∀A.∀P:A → Prop.∀c:Σx:A.P x.A ≝ eject on _c:Σx:?.? to ?.
10
11(*axiom VOID: Type[0].
12axiom assert_false: VOID.
13definition bigbang: ∀A:Type[0].False → VOID → A.
14 #A #abs cases abs
15qed.
16
17coercion bigbang nocomposites: ∀A:Type[0].False → ∀v:VOID.A ≝ bigbang on _v:VOID to ?.*)
18
19lemma sig2: ∀A.∀P:A → Prop. ∀p:Σx:A.P x. P (eject … p).
20 #A #P #p cases p #w #q @q
21qed.
22
23(* END RUSSELL **)
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