Mathlib Map

Theorems · Theorem · logic and foundations

FirstOrder.Language.ClosedUnder.inf

∀ {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
0 results in Mathlib
Foundations
Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FirstOrder.Language.Structure
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Set · cited by 53352SetFirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureFirstOrder.Language.Functions · cited by 153Language.FunctionsFirstOrder.Language.ClosedUnder · cited by 13Language.ClosedUnderFirstOrder.Language.ClosedUnder.inter · cited by 1ClosedUnder.interClosedUnder.infCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.