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].
+definition inject : ∀A.∀P:A → Prop.∀a.∀p:P a.\ 5a title="Sigma" href="cic:/fakeuri.def(1)"\ 6Σ\ 5/a\ 6x:A.P x ≝ λA,P,a,p. \ 5a href="cic:/matita/basics/types/Sig.con(0,1,2)"\ 6dp\ 5/a\ 6 … a p.
+definition eject : ∀A.∀P: A → Prop.(\ 5a title="Sigma" href="cic:/fakeuri.def(1)"\ 6Σ\ 5/a\ 6x: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 ?.
+(* 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.
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).
+lemma sig2: ∀A.∀P:A → Prop. ∀p:\ 5a title="Sigma" href="cic:/fakeuri.def(1)"\ 6Σ\ 5/a\ 6x:A.P x. P (\ 5a href="cic:/matita/Cerco/ASM/JMCoercions/eject.def(1)"\ 6eject\ 5/a\ 6 … p).
#A #P #p cases p #w #q @q
qed.
-(* END RUSSELL **)
+(* END RUSSELL **)
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