map₂Left_eq_map₂Left' — Mathlib

English

For any f : α → Option β → γ and lists as, bs, map₂Left f as bs equals the fst component of map₂Left' f as bs.

Русский

Для любых f : α → Option β → γ и списков as, bs, map₂Left f as bs равен сначалаcой частью пары (fst) from map₂Left' f as bs.

LaTeX

$$$\\forall f:\\alpha \\to \\mathrm{Option}\\,\\beta \\to \\gamma\\ ,\\ \\forall as bs,\\ \\mathrm{map₂Left}\\ f\\ as\\ bs = (\\mathrm{map₂Left}'\\ f\\ as\\ bs).fst$$$

Lean4

theorem map₂Left_eq_map₂Left' : ∀ as bs, map₂Left f as bs = (map₂Left' f as bs).fst
  | [], _ => by simp
  | a :: as, [] => by simp
  | a :: as, b :: bs => by simp [map₂Left_eq_map₂Left']

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