Theorems · Theorem · logic and foundations

FirstOrder.Language.Term.realize_restrictVar

∀ {L : FirstOrder.Language} {M : Type w} [inst : L.Structure M] {α : Type u'} {β : Type v'} [inst_1 : DecidableEq α]
  {t : L.Term α} {f : ↥t.varFinset → β} {v : β → M} (v' : α → M),
  (∀ (a : ↥t.varFinset), v (f a) = v' ↑a) →
    FirstOrder.Language.Term.realize v (t.restrictVar f) = FirstOrder.Language.Term.realize v' t

Defined in

Mathlib.ModelTheory.Semantics

Cited by

1 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FirstOrder.Language.StructureDecidableEq