Theorems · Theorem · logic and foundations
FirstOrder.Language.Theory.ModelsBoundedFormula.realize_boundedFormula
∀ {L : FirstOrder.Language} {T : L.Theory} {α : Type w} {n : ℕ} {φ : L.BoundedFormula α n},
T ⊨ᵇ φ → ∀ (M : Type u_1) [inst : L.Structure M] [M ⊨ T] [Nonempty M] {v : α → M} {xs : Fin n → M}, φ.Realize v xs- Defined in
- Mathlib.ModelTheory.Satisfiability
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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.BoundedFormulastatement and proof · cited by 207
- FirstOrder.Language.Theorystatement and proof · cited by 154
- FirstOrder.Language.BoundedFormula.Realizestatement · cited by 104
- FirstOrder.Language.Formula.Realizeproof · cited by 81
- FirstOrder.Language.Theory.Modelstatement and proof · cited by 67
- FirstOrder.Language.Theory.ModelsBoundedFormulastatement and proof · cited by 30
- FirstOrder.Language.BoundedFormula.toFormulaproof · cited by 6
- FirstOrder.Language.Theory.ModelsBoundedFormula.realize_formulaproof · cited by 2
- FirstOrder.Language.Theory.models_toFormula_iffproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Theory.Iff.realize_bd_iffproof · cited by 5