Theorems · Theorem · order theory
iSup_lt_iff
∀ {α : Type u_1} {ι : Sort u_4} [inst : CompleteSemilatticeSup α] {l : α} {f : ι → α},
iSup f < l ↔ ∃ b < l, ∀ (i : ι), f i ≤ b- Defined in
- Mathlib.Order.CompleteLattice.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext, Quot.sound
- Assumes
- CompleteSemilatticeSup
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.
- iSupstatement · cited by 2,415
- Set.forall_mem_rangeproof · cited by 135
- CompleteSemilatticeSupstatement and proof · cited by 18
- sSup_lt_iffproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Set.exists_isChain_of_le_chainHeightproof · cited by 4
- MeasureTheory.Submartingale.upcrossings_ae_lt_top'proof · cited by 1