diff options
author | herbelin <herbelin@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2003-04-09 11:23:46 +0000 |
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committer | herbelin <herbelin@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2003-04-09 11:23:46 +0000 |
commit | 9075978130301e2bc71b46b7ef7bd34cf5cc076b (patch) | |
tree | 60f597222bc4fe5aa4cf8bed167dc5b18d9ae80c /theories/Logic/Eqdep.v | |
parent | dbdaa57106427ed61d4eff967e0295979ce9a0bf (diff) |
Renommage K; equivalence JMeq et eq_dep sur Type
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@3879 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Logic/Eqdep.v')
-rwxr-xr-x | theories/Logic/Eqdep.v | 16 |
1 files changed, 13 insertions, 3 deletions
diff --git a/theories/Logic/Eqdep.v b/theories/Logic/Eqdep.v index 25ead9897..40a50837d 100755 --- a/theories/Logic/Eqdep.v +++ b/theories/Logic/Eqdep.v @@ -110,19 +110,29 @@ Elim p1 using eq_indd. Apply eq_dep_intro. Qed. -(** Streicher axiom K is a direct instance of UIP *) +(** Uniqueness of Reflexive Identity Proofs is a direct instance of UIP *) -Lemma Streicher_K : (U:Type)(x:U)(p:x=x)p=(refl_equal U x). +Lemma UIP_refl : (U:Type)(x:U)(p:x=x)p=(refl_equal U x). Proof. Intros; Apply UIP. Qed. +(** Streicher axiom K is a direct consequence of Uniqueness of + Reflexive Identity Proofs *) + +Lemma Streicher_K : (U:Type)(x:U)(P:x=x->Prop) + (P (refl_equal ? x))->(p:x=x)(P p). +Proof. +Intros; Rewrite UIP_refl; Assumption. +Qed. + (** We finally recover eq_rec_eq (alternatively eq_rect_eq) from K *) Lemma eq_rec_eq : (U:Type)(P:U->Set)(p:U)(x:(P p))(h:p=p) x=(eq_rec U p P x p h). +Proof. Intros. -Rewrite Streicher_K with p:=h. +Apply Streicher_K with p:=h. Reflexivity. Qed. |