Theorems · Theorem · logic and foundations
FirstOrder.Language.Theory.Model.realize_of_mem
∀ {L : FirstOrder.Language} {M : Type w} {inst : L.Structure M} {T : L.Theory} [self : M ⊨ T], ∀ φ ∈ T, M ⊨ φ- Defined in
- Mathlib.ModelTheory.Semantics
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.Structurestatement and proof · cited by 775
- FirstOrder.Language.Theorystatement and proof · cited by 154
- FirstOrder.Language.Sentencestatement · cited by 127
- FirstOrder.Language.Theory.Modelstatement and proof · cited by 67
- FirstOrder.Language.Sentence.Realizestatement · cited by 62
Cited by3
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Theory.realize_sentence_of_memproof · cited by 11
- FirstOrder.Language.Theory.model_iffproof · cited by 3
- FirstOrder.Language.Theory.CompleteType.false_of_mem_of_not_memproof · cited by 0