Theorems · Theorem · logic and foundations
FirstOrder.Language.Theory.CompleteType.mem_or_not_mem
∀ {L : FirstOrder.Language} {T : L.Theory} {α : Type w} (p : T.CompleteType α) (φ : (L.withConstants α).Sentence),
φ ∈ p ∨ FirstOrder.Language.Formula.not φ ∈ p- Defined in
- Mathlib.ModelTheory.Types
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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.Theorystatement and proof · cited by 154
- FirstOrder.Language.Sentencestatement and proof · cited by 127
- FirstOrder.Language.withConstantsstatement and proof · cited by 108
- FirstOrder.Language.Formulastatement · cited by 93
- FirstOrder.Language.Theory.CompleteTypestatement and proof · cited by 35
- FirstOrder.Language.Formula.notstatement · cited by 27
- FirstOrder.Language.Theory.CompleteType.isMaximalproof · cited by 8
- FirstOrder.Language.Theory.IsMaximal.mem_or_not_memproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Theory.CompleteType.not_mem_iffproof · cited by 1
- FirstOrder.Language.Theory.CompleteType.mem_of_modelsproof · cited by 0