Theorems · Theorem · logic and foundations
FirstOrder.Language.ClosedUnder.inter
∀ {L : FirstOrder.Language} {M : Type w} [inst : L.Structure M] {n : ℕ} {f : L.Functions n} {s t : Set M},
FirstOrder.Language.ClosedUnder f s → FirstOrder.Language.ClosedUnder f t → FirstOrder.Language.ClosedUnder f (s ∩ t)- Defined in
- Mathlib.ModelTheory.Substructures
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
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.
- Setstatement and proof · cited by 53,352
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Structurestatement and proof · cited by 775
- FirstOrder.Language.Functionsstatement and proof · cited by 153
- Set.mem_interproof · cited by 25
- Set.mem_of_mem_inter_rightproof · cited by 13
- FirstOrder.Language.ClosedUnderstatement and proof · cited by 13
- Set.mem_of_mem_inter_leftproof · cited by 10
Cited by1
Results whose statement or proof uses this declaration.
- FirstOrder.Language.ClosedUnder.infproof · cited by 0