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Theorems · Theorem · logic and foundations

FirstOrder.Language.BoundedFormula.IsAtomic.isQF

∀ {L : FirstOrder.Language} {α : Type u'} {n : ℕ} {φ : L.BoundedFormula α n}, φ.IsAtomic → φ.IsQF
Defined in
Mathlib.ModelTheory.Complexity
Cited by
9 results in Mathlib
Foundations
Depth 4 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.Relations.isQF · cited by 5Relations.isQFFirstOrder.Language.BoundedFormula.IsQF.liftAt · cited by 3IsQF.liftAtFirstOrder.Language.BoundedFormula.IsQF.relabel · cited by 1IsQF.relabelFirstOrder.Language.BoundedFormula.IsAtomic.isPrenex · cited by 1IsAtomic.isPrenexFirstOrder.Language.BoundedFormula.IsQF.castLE · cited by 1IsQF.castLEFirstOrder.Language.Relations.isUniversal_antisymmetric · cited by 0Relations.isUniversal_ant…FirstOrder.Language.Relations.isUniversal_irreflexive · cited by 0Relations.isUniversal_irr…FirstOrder.Language.BoundedFormula.IsAtomic.isExistential · cited by 0IsAtomic.isExistentialFirstOrder.Language.BoundedFormula.IsAtomic.isUniversal · cited by 0IsAtomic.isUniversalFirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.BoundedFormula · cited by 207Language.BoundedFormulaFirstOrder.Language.BoundedFormula.IsQF · cited by 36BoundedFormula.IsQFFirstOrder.Language.BoundedFormula.IsAtomic · cited by 22BoundedFormula.IsAtomicIsAtomic.isQFCITED BYCITES

Cites4

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

Cited by9

Results whose statement or proof uses this declaration.