simplicialEvalσ_monotone — Mathlib

English

The function simplicialEvalσ L is monotone in its argument: if a ≤ b then simplicialEvalσ L a ≤ simplicialEvalσ L b.

Русский

Функция simplicialEvalσ L монотонна по аргументу: если a ≤ b, то simplicialEvalσ L a ≤ simplicialEvalσ L b.

LaTeX

$$$\\\\text{Monotone}(\\\\lambda j. \\\\text{simplicialEvalσ}(L,j)).$$$

Lean4

theorem simplicialEvalσ_monotone (L : List ℕ) : Monotone (simplicialEvalσ L) :=
  by
  intro a b hab
  induction L generalizing a b with
  | nil => exact hab
  | cons head tail h_rec => grind [simplicialEvalσ]

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