Definition MonUnit_law (f : Map m1 m2) := f (Munit m1) =_S Munit m2.Definition MonOp_law (f : Map m1 m2) :=
  forall a b : m1, f (a +_M b) =_S f a +_M f b.Structure MonMor : Type := 
  {MonMap :> Map m1 m2;
   Prf_MonUnit_law : MonUnit_law MonMap;
   Prf_MonOp_law : MonOp_law MonMap}.Structure MonMor : Type := 
  {MonMap :> Map m1 m2;
   Prf_MonUnit_law : MonUnit_law MonMap;
   Prf_MonOp_law : MonOp_law MonMap}.Structure MonMor : Type := 
  {MonMap :> Map m1 m2;
   Prf_MonUnit_law : MonUnit_law MonMap;
   Prf_MonOp_law : MonOp_law MonMap}.Structure MonMor : Type := 
  {MonMap :> Map m1 m2;
   Prf_MonUnit_law : MonUnit_law MonMap;
   Prf_MonOp_law : MonOp_law MonMap}.

Lemma MMon_unit : forall f : MonMor, f (Munit m1) =_S Munit m2.