Theorems · Theorem · logic and foundations
FirstOrder.Language.Formula.realize_equivSentence_symm_con
∀ {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.withConstants α).Sentence),
((FirstOrder.Language.Formula.equivSentence.symm φ).Realize fun a => ↑(L.con a)) ↔ M ⊨ φ- Defined in
- Mathlib.ModelTheory.Semantics
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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
- Equiv.symmstatement · cited by 3,681
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Structurestatement and proof · cited by 775
- FirstOrder.Language.BoundedFormulaproof · cited by 207
- FirstOrder.Language.Sentencestatement and proof · cited by 127
- transproof · cited by 111
- FirstOrder.Language.withConstantsstatement and proof · cited by 108
- FirstOrder.Language.BoundedFormula.Realizeproof · cited by 104
- FirstOrder.Language.Formulastatement · cited by 93
- FirstOrder.Language.Formula.Realizestatement · cited by 81
Cited by4
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Formula.realize_equivSentence_symmproof · cited by 3
- FirstOrder.Language.Formula.realize_equivSentenceproof · cited by 2
- FirstOrder.Language.ElementarySubstructure.meetsDefinableproof · cited by 0
- FirstOrder.Language.Theory.exists_modelType_is_realized_inproof · cited by 0