X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Flibrary%2Falgebra%2Fsemigroups.ma;h=539228c8cdef6d600e5741397ce5d3a4020d4275;hb=0b69be40774bf7f75c8ed8a75c02998437ebbdbb;hp=12ff9531155cc31d19e9aecb8b2a44bb8ba4885f;hpb=9e32b487a1343ead9069ea76e40515ceb19d26d6;p=helm.git diff --git a/matita/library/algebra/semigroups.ma b/matita/library/algebra/semigroups.ma index 12ff95311..539228c8c 100644 --- a/matita/library/algebra/semigroups.ma +++ b/matita/library/algebra/semigroups.ma @@ -18,7 +18,7 @@ include "higher_order_defs/functions.ma". (* Magmas *) -record Magma : Type ≝ +record Magma : Type≝ { carrier:> Type; op: carrier → carrier → carrier }. @@ -32,10 +32,10 @@ interpretation "magma operation" 'magma_op a b = (* Semigroups *) -record isSemiGroup (M:Magma) : Prop ≝ +record isSemiGroup (M:Magma) : Prop≝ { op_associative: associative ? (op M) }. -record SemiGroup : Type ≝ +record SemiGroup : Type≝ { magma:> Magma; semigroup_properties:> isSemiGroup magma }. @@ -51,6 +51,6 @@ theorem is_left_unit_to_is_right_unit_to_eq: is_left_unit ? e → is_right_unit ? e' → e=e'. intros; rewrite < (H e'); - rewrite < (H1 e) in \vdash (? ? % ?); + rewrite < (H1 e) in \vdash (? ? % ?). reflexivity. qed.