Theorems · Theorem · order theory
IsGLB.iInf_eq
∀ {α : Type u_1} {ι : Sort u_4} [inst : CompleteLattice α] {f : ι → α} {a : α}, IsGLB (Set.range f) a → ⨅ j, f j = a- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 11 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 and proof · cited by 213
- IsGLB.sInf_eqproof · cited by 14
Cited by1
Results whose statement or proof uses this declaration.
- GaloisConnection.u_iInfproof · cited by 40