(* Magmas *)
-record Magma : Type ≝
+record Magma : Type≝
{ carrier:> Type;
op: carrier → carrier → carrier
}.
(* 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
}.
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.