cons_equiv_eq_equiv_cons — Mathlib

English

For any α, n, a, s, the equality (a :: symEquivSym' s) = symEquivSym' (a ::ₛ s) holds, i.e., the cons operation commutes with the equivalence between Sym and Sym'.

Русский

Для любых α, n, a, s равенство (a :: symEquivSym' s) = symEquivSym' (a ::ₛ s) справедливо; то есть конc и эквив когерентны.

LaTeX

$$$ a ::\, \mathrm{symEquivSym'}(s) = \mathrm{symEquivSym'}(a ::ₛ s). $$$

Lean4

theorem cons_equiv_eq_equiv_cons (α : Type*) (n : ℕ) (a : α) (s : Sym α n) :
    (a :: symEquivSym' s) = symEquivSym' (a ::ₛ s) :=
  by
  rcases s with ⟨⟨l⟩, _⟩
  rfl

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