Theorems · Definition · logic and foundations
FirstOrder.Language.Formula.equivSentence
{L : FirstOrder.Language} → {α : Type u'} → L.Formula α ≃ (L.withConstants α).SentenceA bijection sending formulas to sentences with constants.
- Defined in
- Mathlib.ModelTheory.Syntax
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Equivstatement · cited by 8,337
- Equiv.symmproof · cited by 3,681
- FirstOrder.Languagestatement and proof · cited by 1,084
- Equiv.transproof · cited by 337
- FirstOrder.Language.Sentencestatement · cited by 127
- FirstOrder.Language.withConstantsstatement · cited by 108
- FirstOrder.Language.Formulastatement · cited by 93
- Equiv.sumEmptyproof · cited by 8
- FirstOrder.Language.BoundedFormula.constantsVarsEquivproof · cited by 4
- FirstOrder.Language.BoundedFormula.relabelEquivproof · cited by 1
Cited by11
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Formula.realize_equivSentence_symm_constatement · cited by 4
- FirstOrder.Language.Formula.realize_equivSentence_symmstatement · cited by 3
- FirstOrder.Language.Formula.realize_equivSentencestatement and proof · cited by 2
- FirstOrder.Language.Theory.models_formula_iff_onTheory_models_equivSentencestatement and proof · cited by 1
- FirstOrder.Language.ElementarySubstructure.meetsDefinableproof · cited by 0
- FirstOrder.Language.Theory.CompleteType.mem_typeOfstatement · cited by 0
- FirstOrder.Language.Formula.realize_exClosure_of_realize_equivSentencestatement and proof · cited by 0
- FirstOrder.Language.Formula.equivSentence_infstatement · cited by 0
- FirstOrder.Language.Formula.equivSentence_notstatement · cited by 0
- FirstOrder.Language.Theory.CompleteType.formula_mem_typeOfstatement and proof · cited by 0
- FirstOrder.Language.Formula.exists_realize_equivSentence_iff_realize_exClosurestatement and proof · cited by 0