Theorems · Theorem · logic and foundations
FirstOrder.Language.BoundedFormula.imp_iff_not_sup
∀ {L : FirstOrder.Language} {T : L.Theory} {α : Type w} {n : ℕ} (φ ψ : L.BoundedFormula α n),
T.Iff (φ.imp ψ) (φ.not ⊔ ψ)- Defined in
- Mathlib.ModelTheory.Equivalence
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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.BoundedFormulastatement and proof · cited by 207
- FirstOrder.Language.Theorystatement and proof · cited by 154
- FirstOrder.Language.BoundedFormula.Realizeproof · cited by 104
- FirstOrder.Language.Theory.ModelTypeproof · cited by 62
- FirstOrder.Language.Theory.ModelType.Carrierproof · cited by 59
- FirstOrder.Language.Theory.Iffstatement · cited by 32
- FirstOrder.Language.BoundedFormula.notstatement · cited by 27
Cited by2
Results whose statement or proof uses this declaration.
- FirstOrder.Language.BoundedFormula.IsQF.induction_on_sup_notproof · cited by 1
- FirstOrder.Language.Formula.imp_iff_not_supproof · cited by 0