Theorems · Theorem · order theory
Finset.inf_eq_top_iff
∀ {α : Type u_2} {β : Type u_3} [inst : SemilatticeInf α] [inst_1 : OrderTop α] (f : β → α) (S : Finset β),
S.inf f = ⊤ ↔ ∀ s ∈ S, f s = ⊤- Defined in
- Mathlib.Data.Finset.Lattice.Fold
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 60 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
- Top.topstatement and proof · cited by 9,680
- SemilatticeInfstatement and proof · cited by 634
- OrderTopstatement and proof · cited by 493
- Finset.infstatement and proof · cited by 219
- Finset.inductionproof · cited by 108
- Finset.mem_insertproof · cited by 44
- Finset.notMem_emptyproof · cited by 40
- IsEmpty.forall_iffproof · cited by 39
- Finset.inf_insertproof · cited by 16
- Finset.inf_emptyproof · cited by 15
- inf_eq_top_iffproof · cited by 7
Cited by3
Results whose statement or proof uses this declaration.
- Finset.inf_eq_top_of_isEmptyproof · cited by 1
- Finset.codisjoint_inf_rightproof · cited by 0
- Finset.codisjoint_inf_leftproof · cited by 0