English
Maps induced by surjective homomorphisms with ker containment match the mapGen construction; reused statement as in 120971.
Русский
Преобразование, индуцированное сюръективным гомоморфизмом, совместимо с конструкцией mapGen.
LaTeX
$$$c.mapGen f = c.mapOfSurjective f h hf$$$
Lean4
/-- Given a homomorphism `f` from the quotient of a monoid by a congruence relation, `f` equals the
homomorphism on the quotient induced by `f` composed with the natural map from the monoid to
the quotient. -/
@[to_additive (attr := simp) /-- Given a homomorphism `f` from the quotient of an `AddMonoid` by an
additive congruence relation, `f` equals the homomorphism on the quotient induced by `f` composed
with the natural map from the `AddMonoid` to the quotient. -/
]
theorem lift_apply_mk' (f : c.Quotient →* P) :
(c.lift (f.comp c.mk') fun x y h => show f ↑x = f ↑y by rw [c.eq.2 h]) = f := by ext x; rcases x with ⟨⟩; rfl
