commit by user andrea

[helm.git] / weblib / Cerco / ASM / JMCoercions.ma

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+include "basics/jmeq.ma".
+include "basics/types.ma".
+include "basics/list.ma".
+
+definition inject : ∀A.∀P:A → Prop.∀a.∀p:P a.Σx:A.P x ≝ λA,P,a,p. dp … a p.
+definition eject : ∀A.∀P: A → Prop.(Σx:A.P x) → A ≝ λA,P,c.match c with [ dp w p ⇒ w].
+
+coercion inject nocomposites: ∀A.∀P:A → Prop.∀a.∀p:P a.Σx:A.P x ≝ inject on a:? to Σx:?.?.
+coercion eject nocomposites: ∀A.∀P:A → Prop.∀c:Σx:A.P x.A ≝ eject on _c:Σx:?.? to ?.
+
+(*axiom VOID: Type[0].
+axiom assert_false: VOID.
+definition bigbang: ∀A:Type[0].False → VOID → A.
+ #A #abs cases abs
+qed.
+
+coercion bigbang nocomposites: ∀A:Type[0].False → ∀v:VOID.A ≝ bigbang on _v:VOID to ?.*)
+
+lemma sig2: ∀A.∀P:A → Prop. ∀p:Σx:A.P x. P (eject … p).
+ #A #P #p cases p #w #q @q
+qed.
+
+(* END RUSSELL **)