∀ {α : Type u_1} {M : Type u_2} [inst : Monoid M] (f : α → M) {rels : FreeMonoid α → FreeMonoid α → Prop},
  (∀ (a b : FreeMonoid α), rels a b → (FreeMonoid.lift f) a = (FreeMonoid.lift f) b) →
    conGen rels ≤ Con.ker (FreeMonoid.lift f)