Mathlib Map

Theorems · Theorem · order theory

CountableInfClosed.isGLB_mem

∀ {α : Type u_2} [inst : LE α] {s : Set α},
  CountableInfClosed s → ∀ t ⊆ s, t.Nonempty → t.Countable → ∀ (x : α), IsGLB t x → x ∈ s
Defined in
Mathlib.Order.CountableSupClosed
Cited by
10 results in Mathlib
Foundations
Depth 7 from the axioms · uses no axioms
Assumes
LE
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

CountableInfClosed.iInf_mem · cited by 3CountableInfClosed.iInf_m…CountableInfClosed.infClosed · cited by 3CountableInfClosed.infClo…countableInfClosed_preimage_ofDual · cited by 1countableInfClosed_preima…CountableInfClosed.prod · cited by 1CountableInfClosed.prodcountableSupClosed_preimage_ofDual · cited by 1countableSupClosed_preima…CountableInfClosed.sInter · cited by 1CountableInfClosed.sIntercountableInfClosed_preimage_toDual · cited by 0countableInfClosed_preima…countableInfClosure_eq_sInter · cited by 0countableInfClosure_eq_sI…CountableInfClosed.inter · cited by 0CountableInfClosed.intercountableSupClosed_preimage_toDual · cited by 0countableSupClosed_preima…Set · cited by 53352SetSet.Nonempty · cited by 2627Set.NonemptySet.Countable · cited by 545Set.CountableIsGLB · cited by 213IsGLBCountableInfClosed · cited by 27CountableInfClosedCountableInfClosed.isGLB_memCITED BYCITES

Cites5

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

Cited by10

Results whose statement or proof uses this declaration.