Theorems · Theorem · logic and foundations
FirstOrder.Language.Formula.realize_equivSentence
∀ {L : FirstOrder.Language} (M : Type w) [inst : L.Structure M] {α : Type u'} [inst_1 : (L.withConstants α).Structure M]
[(L.lhomWithConstants α).IsExpansionOn M] (φ : L.Formula α),
M ⊨ FirstOrder.Language.Formula.equivSentence φ ↔ φ.Realize fun a => ↑(L.con a)- Defined in
- Mathlib.ModelTheory.Semantics
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Equivstatement · cited by 8,337
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Structurestatement and proof · cited by 775
- Equiv.symm_apply_applyproof · cited by 320
- FirstOrder.Language.Sentencestatement · cited by 127
- FirstOrder.Language.withConstantsstatement and proof · cited by 108
- FirstOrder.Language.Formulastatement and proof · cited by 93
- FirstOrder.Language.Formula.Realizestatement and proof · cited by 81
- FirstOrder.Language.Sentence.Realizestatement · cited by 62
- FirstOrder.Language.lhomWithConstantsstatement and proof · cited by 39
- FirstOrder.Language.LHom.IsExpansionOnstatement and proof · cited by 31
Cited by2
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Theory.ModelsBoundedFormula.realize_formulaproof · cited by 2