Theorems · Theorem · logic and foundations
FirstOrder.Language.Substructure.subset_closure_withConstants
∀ {L : FirstOrder.Language} {M : Type w} [inst : L.Structure M] {A s : Set M},
A ⊆ ↑((FirstOrder.Language.Substructure.closure (L.withConstants ↑A)).toFun s)- Defined in
- Mathlib.ModelTheory.Substructures
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 69 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
- Set.Elemstatement and proof · cited by 7,166
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Structurestatement and proof · cited by 775
- FirstOrder.Language.Substructurestatement · cited by 242
- FirstOrder.Language.withConstantsstatement and proof · cited by 108
- LowerAdjoint.toFunstatement · cited by 105
- FirstOrder.Language.Substructure.closurestatement · cited by 70
- FirstOrder.Language.Constantsproof · cited by 14
- FirstOrder.Language.Substructure.constants_memproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Substructure.closure_withConstants_eqproof · cited by 0