Theorems · Theorem · logic and foundations
FirstOrder.Language.Sentence.realize_not
∀ {L : FirstOrder.Language} (M : Type w) [inst : L.Structure M] {φ : L.Sentence},
M ⊨ FirstOrder.Language.Formula.not φ ↔ ¬M ⊨ φ- Defined in
- Mathlib.ModelTheory.Semantics
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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.notstatement · cited by 27
Cited by6
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Theory.models_iff_not_satisfiableproof · cited by 4
- FirstOrder.Language.Theory.IsComplete.realize_sentence_iffproof · cited by 3
- Cardinal.Categorical.isCompleteproof · cited by 3
- FirstOrder.Language.Theory.IsComplete.eq_complete_theoryproof · cited by 2
- FirstOrder.Language.realize_iff_of_model_completeTheoryproof · cited by 0