Theorems · Theorem · logic and foundations

FirstOrder.Language.Formula.exists_realize_equivSentence_iff_realize_exClosure

∀ {L : FirstOrder.Language} {M : Type w} [inst : L.Structure M] {α : Type u'} [inst_1 : DecidableEq α] [Nonempty M]
  {φ : L.Formula α}, (∃ v, M ⊨ FirstOrder.Language.Formula.equivSentence φ) ↔ M ⊨ φ.exClosure

Defined in

Mathlib.ModelTheory.Semantics

Cited by

0 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FirstOrder.Language.StructureDecidableEqNonempty