X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fnlibrary%2Fbasics%2Feq.ma;h=61047a474ca5ca1516d56c982de7d09e2a3c3de2;hb=63047f8ff8ef477ac32939985b0b41b70e918054;hp=73abc9f09c2098b14ff5982f7deef0aedda47ccd;hpb=34311f3f810eb893b865d1893eae1cf62cd490b4;p=helm.git diff --git a/helm/software/matita/nlibrary/basics/eq.ma b/helm/software/matita/nlibrary/basics/eq.ma index 73abc9f09..61047a474 100644 --- a/helm/software/matita/nlibrary/basics/eq.ma +++ b/helm/software/matita/nlibrary/basics/eq.ma @@ -25,8 +25,17 @@ ntheorem symmetric_eq: ∀A:Type. symmetric A (eq A). ntheorem transitive_eq : ∀A:Type. transitive A (eq A). #A; #x; #y; #z; #H1; #H2; nrewrite > H1; //; nqed. +(* ntheorem symmetric_not_eq: ∀A:Type. symmetric A (λx,y.x ≠ y). +/3/; nqed. +*) + +ntheorem symmetric_not_eq: ∀A:Type. ∀x,y:A. x ≠ y → y ≠ x. +/3/; nqed. + +(* #A; #x; #y; #H; #K; napply H; napply symmetric_eq; //; nqed. +*) ntheorem eq_f: ∀A,B:Type.∀f:A→B.∀x,y:A. x=y → f x = f y. #A; #B; #f; #x; #y; #H; nrewrite > H; //; nqed.