sum_equiv_comp_eval_eq_elim — Mathlib

English

Any x in C' has the value false at the distinguished term.

Русский

Любой x из C' имеет значение false в заданной точке.

LaTeX

$$$\\forall x:\\I,\\ x\\in C' C ho \\Rightarrow x(\\mathrm{term}\\ I ho) = \\mathrm{false}$$$

Lean4

theorem sum_equiv_comp_eval_eq_elim :
    eval C ∘ (sum_equiv C hsC ho).toFun =
      (Sum.elim (fun (l : GoodProducts (π C (ord I · < o))) ↦ Products.eval C l.1)
        (fun (l : MaxProducts C ho) ↦ Products.eval C l.1)) :=
  by ext ⟨_, _⟩ <;> [rfl; rfl]

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