English
A congruence principle for mkInductiveAux₂, showing that, provided the same initial data, the result at n is determined up to equality by the recursive definition.
Русский
Принцип эквивалентности для mkInductiveAux₂: полученная структура на n определяется равенством при заданной начальной информации и рекурсивном определении.
LaTeX
$$$\forall n,\ Eq (mkInductiveAux₂\ e\ zero\ comm_zero\ one\ comm_one\ succ\ n)\ (mkInductiveAux₂\ e\ zero\ comm_zero\ one\ comm_one\ succ\ n).$$$
Lean4
theorem mkInductiveAux₃ (i j : ℕ) (h : i + 1 = j) :
(mkInductiveAux₂ e zero comm_zero one comm_one succ i).2.1 ≫ (Q.xPrevIso h).hom =
(P.xNextIso h).inv ≫ (mkInductiveAux₂ e zero comm_zero one comm_one succ j).1 :=
by
subst j
rcases i with (_ | _ | i) <;> simp [mkInductiveAux₂]
