Theorems · Theorem · order theory
iInf_lt_iff
∀ {α : Type u_1} {ι : Sort u_4} [inst : CompleteLinearOrder α] {a : α} {f : ι → α}, iInf f < a ↔ ∃ i, f i < a- Defined in
- Mathlib.Order.CompleteLattice.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CompleteLinearOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- iInfstatement · cited by 1,690
- CompleteLinearOrderstatement and proof · cited by 126
- Set.exists_range_iffproof · cited by 22
- sInf_lt_iffproof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- ENat.iInf_eq_zeroproof · cited by 1
- lt_biInf_iffproof · cited by 0