X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Flib%2Fbasics%2Fjmeq.ma;h=42e52c0a430a40ee20a133a2f23c283bff7b00e2;hb=c2c729ed092b9bad8b004bb8f8dea6e0f4471995;hp=a520ca96ff8964d0c38c7efb26b97c77605b0ace;hpb=8ea6d456f9e71babcf5adb2caee6ddd2b95047fb;p=helm.git diff --git a/matita/matita/lib/basics/jmeq.ma b/matita/matita/lib/basics/jmeq.ma index a520ca96f..42e52c0a4 100644 --- a/matita/matita/lib/basics/jmeq.ma +++ b/matita/matita/lib/basics/jmeq.ma @@ -11,10 +11,10 @@ include "basics/logic.ma". -inductive Sigma: Type[1] ≝ - mk_Sigma: ∀p1: Type[0]. p1 → Sigma. +inductive Sigma: Type[2] ≝ + mk_Sigma: ∀p1: Type[1]. p1 → Sigma. -definition p1: Sigma → Type[0]. +definition p1: Sigma → Type[1]. #S cases S #Y #_ @Y qed. @@ -22,7 +22,7 @@ definition p2: ∀S:Sigma. p1 S. #S cases S #Y #x @x qed. -inductive jmeq (A:Type[0]) (x:A) : ∀B:Type[0]. B →Prop ≝ +inductive jmeq (A:Type[1]) (x:A) : ∀B:Type[1]. B →Prop ≝ refl_jmeq : jmeq A x A x. notation < "hvbox(term 46 a break maction (≃) (≃\sub(t,u)) term 46 b)" @@ -43,7 +43,7 @@ lemma K : ∀A.∀x:A.∀h:x=x. eqProp ? h (refl A x). qed. definition cast: - ∀A,B:Type[0].∀E:A=B. A → B. + ∀A,B:Type[1].∀E:A=B. A → B. #A #B #E cases E #X @X qed. @@ -57,7 +57,7 @@ qed. lemma gral: ∀A.∀x,y:A. mk_Sigma A x = mk_Sigma A y → x=y. #A #x #y #E lapply (tech1 ?? E) - generalize in ⊢ (??(???%?)? → ?) #E1 + generalize in ⊢ (??(???%?)? → ?); #E1 normalize in E1; >(K ?? E1) normalize #H @H qed. @@ -100,14 +100,14 @@ qed. lemma jmeq_elim : ∀A.∀x:A.∀P:∀y:A.jmeq A x A y→Type[0]. P x (refl_jmeq A x) → ∀y.∀h:jmeq A x A y.P y h ≝ E. -lemma jmeq_to_eq: ∀A:Type[0]. ∀x,y:A. x≃y → x=y. +lemma jmeq_to_eq: ∀A:Type[1]. ∀x,y:A. x≃y → x=y. #A #x #y #JMEQ @(jmeq_elim ? x … JMEQ) % qed. -coercion jmeq_to_eq: ∀A:Type[0]. ∀x,y:A. ∀p:x≃y.x=y ≝ jmeq_to_eq on _p:?≃? to ?=?. +coercion jmeq_to_eq: ∀A:Type[1]. ∀x,y:A. ∀p:x≃y.x=y ≝ jmeq_to_eq on _p:?≃? to ?=?. lemma eq_to_jmeq: - ∀A: Type[0]. + ∀A: Type[1]. ∀x, y: A. x = y → x ≃ y. //