X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Flibrary%2Falgebra%2Fmonoids.ma;h=fe35eeb6709fea8092269d6035f470f6136c9523;hb=0e9f9d6d7a0466ee132553fb7a983eac282fb12f;hp=a80ee5fb06e40723f2f9e6051c255b9a3fa2a36d;hpb=7815a9150b5581f60e49ad6520f46ac287e073fa;p=helm.git diff --git a/helm/software/matita/library/algebra/monoids.ma b/helm/software/matita/library/algebra/monoids.ma index a80ee5fb0..fe35eeb67 100644 --- a/helm/software/matita/library/algebra/monoids.ma +++ b/helm/software/matita/library/algebra/monoids.ma @@ -12,8 +12,6 @@ (* *) (**************************************************************************) -set "baseuri" "cic:/matita/algebra/monoids/". - include "algebra/semigroups.ma". record PreMonoid : Type ≝ @@ -34,21 +32,17 @@ record Monoid : Type ≝ monoid_properties:> isMonoid premonoid }. -notation "1" with precedence 89 -for @{ 'munit }. - -interpretation "Monoid unit" 'munit = - (cic:/matita/algebra/monoids/e.con _). +interpretation "Monoid unit" 'neutral = (e _). definition is_left_inverse ≝ λM:Monoid. λopp: M → M. - ∀x:M. (opp x)·x = 1. + ∀x:M. (opp x)·x = ⅇ. definition is_right_inverse ≝ λM:Monoid. λopp: M → M. - ∀x:M. x·(opp x) = 1. + ∀x:M. x·(opp x) = ⅇ. theorem is_left_inverse_to_is_right_inverse_to_eq: ∀M:Monoid. ∀l,r.