Mathlib Map

Theorems · Theorem · logic and foundations

FirstOrder.Language.BoundedFormula.IsQF.not

∀ {L : FirstOrder.Language} {α : Type u'} {n : ℕ} {φ : L.BoundedFormula α n}, φ.IsQF → φ.not.IsQF
Defined in
Mathlib.ModelTheory.Complexity
Cited by
4 results in Mathlib
Foundations
Depth 5 from the axioms · uses no axioms
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

FirstOrder.Language.BoundedFormula.IsQF.sup · cited by 1IsQF.supFirstOrder.Language.BoundedFormula.IsQF.top · cited by 0IsQF.topFirstOrder.Language.BoundedFormula.IsQF.inf · cited by 0IsQF.infFirstOrder.Language.Relations.isUniversal_irreflexive · cited by 0Relations.isUniversal_irr…FirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.BoundedFormula · cited by 207Language.BoundedFormulaFirstOrder.Language.BoundedFormula.IsQF · cited by 36BoundedFormula.IsQFFirstOrder.Language.BoundedFormula.not · cited by 27BoundedFormula.notFirstOrder.Language.BoundedFormula.isQF_bot · cited by 6BoundedFormula.isQF_botIsQF.notCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by4

Results whose statement or proof uses this declaration.