Theorems · Definition · logic and foundations
FirstOrder.Language.Formula.Realize
{L : FirstOrder.Language} → {M : Type w} → [L.Structure M] → {α : Type u'} → L.Formula α → (α → M) → PropA formula can be evaluated as true or false by giving values to each free variable.
- Defined in
- Mathlib.ModelTheory.Semantics
- Cited by
- 81 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Structurestatement and proof · cited by 775
- FirstOrder.Language.BoundedFormula.Realizeproof · cited by 104
- FirstOrder.Language.Formulastatement and proof · cited by 93
Cited by89
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Sentence.Realizeproof · cited by 62
- Set.Definableproof · cited by 39
- FirstOrder.Language.Substructure.IsElementaryproof · cited by 8
- Set.Definable.preimage_compproof · cited by 6
- FirstOrder.Language.ElementaryEmbedding.map_formulastatement and proof · cited by 5
- Set.Definable.interproof · cited by 5
- FirstOrder.Language.Formula.realize_equivSentence_symm_constatement · cited by 4
- FirstOrder.Language.Formula.realize_equivSentence_symmstatement · cited by 3
- FirstOrder.Language.ElementaryEmbedding.map_sentenceproof · cited by 3
- FirstOrder.Language.StrongHomClass.realize_sentenceproof · cited by 3
- Set.Definable.complproof · cited by 3
- Set.Definable.unionproof · cited by 3