Last change
on this file since 1489 was
1335,
checked in by sacerdot, 9 years ago

Ported to new Matita stdlib.

File size:
823 bytes

Line  

1  include "basics/jmeq.ma". 

2  include "basics/types.ma". 

3  include "basics/list.ma". 

4  

5  definition inject : ∀A.∀P:A → Prop.∀a.∀p:P a.Σx:A.P x ≝ λA,P,a,p. dp … a p. 

6  definition eject : ∀A.∀P: A → Prop.(Σx:A.P x) → A ≝ λA,P,c.match c with [ dp w p ⇒ w]. 

7  

8  coercion inject nocomposites: ∀A.∀P:A → Prop.∀a.∀p:P a.Σx:A.P x ≝ inject on a:? to Σx:?.?. 

9  coercion eject nocomposites: ∀A.∀P:A → Prop.∀c:Σx:A.P x.A ≝ eject on _c:Σx:?.? to ?. 

10  

11  (*axiom VOID: Type[0]. 

12  axiom assert_false: VOID. 

13  definition bigbang: ∀A:Type[0].False → VOID → A. 

14  #A #abs cases abs 

15  qed. 

16  

17  coercion bigbang nocomposites: ∀A:Type[0].False → ∀v:VOID.A ≝ bigbang on _v:VOID to ?.*) 

18  

19  lemma sig2: ∀A.∀P:A → Prop. ∀p:Σx:A.P x. P (eject … p). 

20  #A #P #p cases p #w #q @q 

21  qed. 

22  

23  (* END RUSSELL **) 

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