Theorems · Theorem · order theory
ciInf_eq_iff
∀ {α : Type u_1} {ι : Sort u_4} [inst : ConditionallyCompleteLinearOrder α] [WellFoundedLT α] [Nonempty ι] (f : ι → α)
(n : α), ⨅ i, f i = n ↔ (∃ i, f i = n) ∧ ∀ (i : ι), n ≤ f i- Cited by
- 1 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.rangeproof · cited by 4,705
- le_antisymmproof · cited by 2,068
- iInfstatement and proof · cited by 1,690
- OrderBotproof · cited by 1,055
- ConditionallyCompleteLinearOrderstatement and proof · cited by 542
- WellFoundedLTstatement and proof · cited by 491
- le_ciInfproof · cited by 32
- OrderBot.bddBelowproof · cited by 31
- ciInf_leproof · cited by 25
- WellFoundedLT.toOrderBotproof · cited by 8
- ciInf_memproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- ENat.iInf_eq_natCast_iffproof · cited by 1