mk_naturality — Mathlib

English

A matching lemma aligning mk.naturality with the global toNerve₂ construction ensures consistency across the nerve.

Русский

Сопоставляющая лемма согласует mk.naturality с общей конструкцией toNerve₂, обеспечивая согласованность по нерву.

LaTeX

$$$mk\_naturality \, = \, toNerve\_2.mk\_naturality$$$

Lean4

/-- A proof that the components defined by `toNerve₂.mk.app` are natural. -/
theorem mk_naturality : toNerve₂.mk.naturalityProperty F = ⊤ :=
  Truncated.morphismProperty_eq_top (toNerve₂.mk.naturalityProperty F)
    (fun
      | 0, _, _ => toNerve₂.mk_naturality_δ0i F _
      | 1, _, _ => toNerve₂.mk_naturality_δ1i F hyp _)
    (fun
      | 0, _, 0 => toNerve₂.mk_naturality_σ00 F
      | 1, _, _ => toNerve₂.mk_naturality_σ1i F hyp _)

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