Theorems · Theorem · logic and foundations
FirstOrder.Language.Theory.Iff.realize_iff
∀ {L : FirstOrder.Language} {T : L.Theory} {α : Type w} {φ ψ : L.Formula α} {M : Type u_2} [Nonempty M]
[inst : L.Structure M] [M ⊨ T], T.Iff φ ψ → ∀ {v : α → M}, φ.Realize v ↔ ψ.Realize v- Defined in
- Mathlib.ModelTheory.Equivalence
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, 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.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.Theory.Iffstatement and proof · cited by 32
- FirstOrder.Language.Theory.Iff.realize_bd_iffproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Theory.Iff.models_sentence_iffproof · cited by 0