Theorems · Theorem · order theory
Finset.inf_lt_iff
∀ {α : Type u_2} {ι : Type u_5} [inst : LinearOrder α] [inst_1 : OrderTop α] {s : Finset ι} {f : ι → α} {a : α},
s.inf f < a ↔ ∃ b ∈ s, f b < a- Defined in
- Mathlib.Data.Finset.Lattice.Fold
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrderOrderTop
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
- LinearOrderstatement and proof · cited by 8,572
- OrderTopstatement and proof · cited by 493
- Finset.consproof · cited by 221
- Finset.infstatement and proof · cited by 219
- Finset.cons_inductionproof · cited by 85
- Finset.mem_consproof · cited by 35
- Finset.inf_leproof · cited by 23
- not_top_ltproof · cited by 17
- Finset.inf_consproof · cited by 16
- lt_of_lt_of_le'proof · cited by 15
- inf_lt_iffproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Finset.inf'_lt_iffproof · cited by 0