Theorems · Theorem · logic and foundations
FirstOrder.Language.Theory.models_formula_iff
∀ {L : FirstOrder.Language} {T : L.Theory} {α : Type w} {φ : L.Formula α},
T ⊨ᵇ φ ↔ ∀ (M : T.ModelType) (v : α → ↑M), φ.Realize v- Defined in
- Mathlib.ModelTheory.Satisfiability
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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.Theorystatement and proof · cited by 154
- FirstOrder.Language.Formulastatement and proof · cited by 93
- FirstOrder.Language.Formula.Realizestatement · cited by 81
- FirstOrder.Language.Theory.ModelTypestatement and proof · cited by 62
- FirstOrder.Language.Theory.ModelType.Carrierstatement and proof · cited by 59
- FirstOrder.Language.Theory.ModelsBoundedFormulastatement · cited by 30
- Unique.forall_iffproof · cited by 13
Cited by2
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Theory.models_sentence_iffproof · cited by 6