Theorems · Theorem · logic and foundations
FirstOrder.Language.Substructure.mem_closed_of_isRelational
∀ (L : FirstOrder.Language) {M : Type w} [inst : L.Structure M] [L.IsRelational] (s : Set M),
s ∈ (FirstOrder.Language.Substructure.closure L).closed- Defined in
- Mathlib.ModelTheory.Substructures
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- SetLike.coestatement · cited by 8,199
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Structurestatement and proof · cited by 775
- FirstOrder.Language.Substructurestatement · cited by 242
- FirstOrder.Language.Functionsproof · cited by 153
- FirstOrder.Language.Substructure.closurestatement · cited by 70
- isEmptyElimproof · cited by 59
- FirstOrder.Language.IsRelationalstatement and proof · cited by 10
- LowerAdjoint.closedstatement · cited by 9
- FirstOrder.Language.Substructure.mem_closed_iffproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Substructure.closure_eq_of_isRelationalproof · cited by 2
- FirstOrder.Language.dlo_isExtensionPairproof · cited by 1