Theorems · Definition · logic and foundations
FirstOrder.Language.Formula.not
{L : FirstOrder.Language} → {α : Type u'} → L.Formula α → L.Formula αThe negation of a formula.
- Defined in
- Mathlib.ModelTheory.Syntax
- Cited by
- 27 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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.Formulastatement and proof · cited by 93
- FirstOrder.Language.BoundedFormula.notproof · cited by 27
Cited by30
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Theory.IsCompleteproof · cited by 11
- FirstOrder.Language.Theory.IsMaximalproof · cited by 10
- FirstOrder.Language.distinctConstantsTheoryproof · cited by 9
- FirstOrder.Language.Sentence.realize_notstatement · cited by 6
- FirstOrder.Language.Theory.ModelsBoundedFormula.realize_sentenceproof · cited by 5
- FirstOrder.Language.Theory.models_iff_not_satisfiablestatement and proof · cited by 4
- Cardinal.Categorical.isCompleteproof · cited by 3
- FirstOrder.Language.Theory.CompleteType.compl_setOfPred_memstatement · cited by 3
- Set.Definable.complproof · cited by 3
- FirstOrder.Language.Theory.IsComplete.realize_sentence_iffproof · cited by 3
- FirstOrder.Language.model_distinctConstantsTheoryproof · cited by 2
- FirstOrder.Language.Theory.CompleteType.mem_or_not_memstatement · cited by 2