Theorems · Theorem · logic and foundations

FirstOrder.Language.BoundedFormula.realize_iAlls

∀ {L : FirstOrder.Language} {M : Type w} [inst : L.Structure M] {α : Type u'} {β : Type v'} [inst_1 : Finite β]
  {φ : L.Formula (α ⊕ β)} {v : α → M} {v' : Fin 0 → M},
  FirstOrder.Language.BoundedFormula.Realize (FirstOrder.Language.Formula.iAlls β φ) v v' ↔
    ∀ (i : β → M), φ.Realize fun a => Sum.elim v i a

Defined in

Mathlib.ModelTheory.Semantics

Cited by

0 results in Mathlib

Foundations

Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FirstOrder.Language.StructureFinite