Theorems · Theorem · order theory
Finset.isGLB_inf
∀ {α : Type u_2} {β : Type u_3} [inst : SemilatticeInf α] [inst_1 : OrderTop α] {s : Finset β} {f : β → α},
IsGLB (f '' ↑s) (s.inf f)- Defined in
- Mathlib.Data.Finset.Lattice.Fold
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemilatticeInfOrderTop
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- Set.ofPredproof · cited by 6,101
- Set.imagestatement · cited by 5,609
- SemilatticeInfstatement and proof · cited by 634
- OrderTopstatement and proof · cited by 493
- SetLike.mem_coeproof · cited by 302
- Finset.infstatement and proof · cited by 219
- IsGLBstatement · cited by 213
- Set.mem_imageproof · cited by 131
- Finset.inf_leproof · cited by 23
- Finset.le_inf_iffproof · cited by 12
Cited by1
Results whose statement or proof uses this declaration.
- Finset.isGLB_inf_idproof · cited by 0