Theorems · Theorem · logic and foundations
FirstOrder.Language.Theory.ModelsBoundedFormula.realize_formula
∀ {L : FirstOrder.Language} {T : L.Theory} {α : Type w} {φ : L.Formula α},
T ⊨ᵇ φ → ∀ (M : Type u_1) [inst : L.Structure M] [M ⊨ T] [Nonempty M] {v : α → M}, φ.Realize v- Defined in
- Mathlib.ModelTheory.Satisfiability
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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.Theorystatement and proof · cited by 154
- FirstOrder.Language.Formulastatement and proof · cited by 93
- FirstOrder.Language.Formula.Realizestatement · cited by 81
- FirstOrder.Language.Theory.Modelstatement and proof · cited by 67
- FirstOrder.Language.lhomWithConstantsproof · cited by 39
- FirstOrder.Language.Theory.ModelsBoundedFormulastatement and proof · cited by 30
- FirstOrder.Language.LHom.onTheoryproof · cited by 27
- FirstOrder.Language.constantsOnproof · cited by 22
- FirstOrder.Language.constantsOn.structureproof · cited by 6
- FirstOrder.Language.Theory.ModelsBoundedFormula.realize_sentenceproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Theory.models_toFormula_iffproof · cited by 1
- FirstOrder.Language.Theory.ModelsBoundedFormula.realize_boundedFormulaproof · cited by 1