Mathlib Map

Theorems · Theorem · logic and foundations

FirstOrder.Language.BoundedFormula.IsAtomic.castLE

∀ {L : FirstOrder.Language} {α : Type u'} {n l : ℕ} {φ : L.BoundedFormula α l} {h : l ≤ n},
  φ.IsAtomic → (FirstOrder.Language.BoundedFormula.castLE h φ).IsAtomic
Defined in
Mathlib.ModelTheory.Complexity
Cited by
1 results in Mathlib
Foundations
Depth 25 from the axioms · uses propext, Quot.sound
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

FirstOrder.Language.BoundedFormula.IsQF.castLE · cited by 1IsQF.castLEFirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.BoundedFormula · cited by 207Language.BoundedFormulaFirstOrder.Language.Term · cited by 166Language.TermFirstOrder.Language.Relations · cited by 147Language.RelationsFirstOrder.Language.Term.relabel · cited by 27Term.relabelFirstOrder.Language.BoundedFormula.IsAtomic · cited by 22BoundedFormula.IsAtomicFirstOrder.Language.BoundedFormula.castLE · cited by 13BoundedFormula.castLEFirstOrder.Language.BoundedFormula.IsAtomic.recOn · cited by 3IsAtomic.recOnIsAtomic.castLECITED BYCITES

Cites8

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

Cited by1

Results whose statement or proof uses this declaration.