realize_term — Mathlib

English

For a general L →ᴸ L′ expansion φ, the onTerm operation commutes with realization: the realization of φ.onTerm t equals the realization of t.

Русский

Для общего расширения φ, операция onTerm commuting с реализацией: реализация φ.onTerm t равна реализации t.

LaTeX

$$$ (\phi.onTerm t).realize v = t.realize v $$$

Lean4

@[simp]
theorem realize_term {F : Type*} [FunLike F M N] [HomClass L F M N] (g : F) {t : L.Term α} {v : α → M} :
    t.realize (g ∘ v) = g (t.realize v) := by
  induction t
  · rfl
  · rw [Term.realize, Term.realize, HomClass.map_fun]
    refine congr rfl ?_
    ext x
    simp [*]

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