proposition: Lemma inject_epi `{Setoid A} `{Equiv B} `{SgOp B} `{MonUnit B} (f g: sq A → B) `{!Monoid_Morphism f} `{!Monoid_Morphism g} : f ∘ inject A = g ∘ inject A → f = g.
proof: Proof. Proof with intuition. intros. pose proof (setoidmor_a f). pose proof (monmor_b (f:=g)). pose proof (sequence_only_extend_commutes sq (f ∘ inject A) _) as E. pose proof (_ : Setoid_Morphism (f ∘ inject A)) as cm. rewrite (E f), (E g)... apply (sequence_extend_morphism sq)... apply cm. apply cm. Qed.
imports: MathClasses.theory.categories MathClasses.interfaces.functors MathClasses.interfaces.abstract_algebra MathClasses.interfaces.sequences