Theorems · Theorem · logic and foundations
FirstOrder.Language.Sentence.realize_iff
∀ {L : FirstOrder.Language} (M : Type w) [inst : L.Structure M] {φ ψ : L.Sentence},
M ⊨ FirstOrder.Language.Formula.iff φ ψ ↔ (M ⊨ φ ↔ M ⊨ ψ)- Defined in
- Mathlib.ModelTheory.Semantics
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.Sentencestatement and proof · cited by 127
- FirstOrder.Language.Sentence.Realizestatement · cited by 62
- FirstOrder.Language.Formula.iffstatement · cited by 2
- FirstOrder.Language.Formula.realize_iffproof · cited by 1
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.