Theorems · Theorem · order theory
iSup_le_iff
∀ {α : Type u_1} {ι : Sort u_4} [inst : CompleteLattice α] {f : ι → α} {a : α}, iSup f ≤ a ↔ ∀ (i : ι), f i ≤ a- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 45 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext, Quot.sound
- Assumes
- CompleteLattice
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.
- iSupstatement · cited by 2,415
- CompleteLatticestatement and proof · cited by 1,048
- Set.forall_mem_rangeproof · cited by 135
- isLUB_le_iffproof · cited by 24
- isLUB_iSupproof · cited by 6
Cited by45
Results whose statement or proof uses this declaration.
- SimpleGraph.eccent_topproof · cited by 4
- Order.krullDim_eq_bot_iffproof · cited by 4
- MulAction.IwasawaStructure.commutator_leproof · cited by 4
- Module.length_compositionSeriesproof · cited by 4
- normalClosure_le_iffproof · cited by 3
- Equiv.Perm.OnCycleFactors.kerParam_range_eqproof · cited by 3
- ringKrullDim_quotient_succ_le_of_nonZeroDivisorproof · cited by 3
- Module.supportDim_le_supportDim_quotSMulTop_succ_of_mem_jacobsonproof · cited by 2
- MeasureTheory.lintegral_const_mul_leproof · cited by 2
- AlgebraicGeometry.isIso_pushoutSection_of_iSup_eqproof · cited by 2
- AntilipschitzWith.hausdorffMeasure_preimage_leproof · cited by 2