Theorems · Theorem · order theory
isGLB_iInf
∀ {α : Type u_1} {ι : Sort u_4} [inst : CompleteLattice α] {f : ι → α}, IsGLB (Set.range f) (⨅ j, f j)- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.rangestatement and proof · cited by 4,705
- iInfstatement · cited by 1,690
- CompleteLatticestatement and proof · cited by 1,048
- IsGLBstatement · cited by 213
- isGLB_sInfproof · cited by 23
Cited by7
Results whose statement or proof uses this declaration.
- le_iInf_iffproof · cited by 30
- isGLB_biInfproof · cited by 4
- CountableInfClosed.iInf_memproof · cited by 3
- iUnion_Ici_eq_Ici_iInfproof · cited by 1
- iUnion_Ici_eq_Ioi_iInfproof · cited by 1
- CountableInfClosed.of_iInf_memproof · cited by 1
- iUnion_Ioi_eq_Ioi_iInfproof · cited by 0