Theorems · Inductive type · logic and foundations
FirstOrder.Language.BoundedFormula.IsAtomic
{L : FirstOrder.Language} → {α : Type u'} → {n : ℕ} → L.BoundedFormula α n → PropAn atomic formula is either equality or a relation symbol applied to terms.
Note that ⊥ and ⊤ are not considered atomic in this convention.
- Defined in
- Mathlib.ModelTheory.Complexity
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- FirstOrder.Languagestatement · cited by 1,084
- FirstOrder.Language.BoundedFormulastatement · cited by 207
Cited by27
Results whose statement or proof uses this declaration.
- FirstOrder.Language.BoundedFormula.IsAtomic.isQFstatement · cited by 9
- FirstOrder.Language.BoundedFormula.IsQF.recOnstatement and proof · cited by 4
- FirstOrder.Language.BoundedFormula.IsQF.liftAtproof · cited by 3
- FirstOrder.Language.BoundedFormula.IsAtomic.recOnstatement and proof · cited by 3
- FirstOrder.Language.BoundedFormula.IsQF.realize_embeddingproof · cited by 2
- FirstOrder.Language.Relations.isAtomicstatement · cited by 2
- FirstOrder.Language.BoundedFormula.IsAtomic.casesOnstatement and proof · cited by 2
- FirstOrder.Language.BoundedFormula.IsQF.casesOnstatement and proof · cited by 2
- FirstOrder.Language.BoundedFormula.IsQF.induction_on_sup_notstatement and proof · cited by 1
- FirstOrder.Language.BoundedFormula.IsQF.relabelproof · cited by 1
- FirstOrder.Language.BoundedFormula.IsAtomic.castLEstatement and proof · cited by 1
- FirstOrder.Language.BoundedFormula.IsAtomic.isPrenexstatement and proof · cited by 1