Theorems · Theorem · order theory
iInf_eq_bot
∀ {α : Type u_1} {ι : Sort u_4} [inst : CompleteLinearOrder α] {f : ι → α}, iInf f = ⊥ ↔ ∀ (b : α), ⊥ < b → ∃ i, f i < b- Defined in
- Mathlib.Order.CompleteLattice.Defs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 18 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Bot.botstatement and proof · cited by 4,720
- iInfstatement · cited by 1,690
- eq_bot_iffproof · cited by 159
- CompleteLinearOrderstatement and proof · cited by 126
- iInf_le_iff_forall_ltproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- iInf₂_eq_botproof · cited by 4
- ENNReal.mul_iInf'proof · cited by 3
- ENat.sub_iSupproof · cited by 0
- ENNReal.sub_iSupproof · cited by 0
- ENNReal.ofReal_iInfproof · cited by 0