Theorems · Theorem · logic and foundations

FirstOrder.Language.LHom.realize_onBoundedFormula

∀ {L : FirstOrder.Language} {L' : FirstOrder.Language} {M : Type w} [inst : L.Structure M] {α : Type u'}
  [inst_1 : L'.Structure M] (φ : L →ᴸ L') [φ.IsExpansionOn M] {n : ℕ} (ψ : L.BoundedFormula α n) {v : α → M}
  {xs : Fin n → M}, (φ.onBoundedFormula ψ).Realize v xs ↔ ψ.Realize v xs

Defined in

Mathlib.ModelTheory.Semantics

Cited by

2 results in Mathlib

Foundations

Depth 23 from the axioms · uses propext, Quot.sound

Assumes

FirstOrder.Language.StructureFirstOrder.Language.StructureFirstOrder.Language.LHom.IsExpansionOn