Theorems · Theorem · order theory
iSup_const
∀ {α : Type u_1} {ι : Sort u_4} [inst : CompleteLattice α] {a : α} [Nonempty ι], ⨆ x, a = a- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext, Quot.sound
- Assumes
- CompleteLatticeNonempty
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- iSupstatement · cited by 2,415
- CompleteLatticestatement and proof · cited by 1,048
- SupSet.sSupproof · cited by 954
- Set.range_constproof · cited by 25
- sSup_singletonproof · cited by 14
Cited by13
Results whose statement or proof uses this declaration.
- Set.iUnion_constproof · cited by 11
- ProbabilityTheory.Kernel.indep_iSup_limsupproof · cited by 3
- iSup_supproof · cited by 3
- iSup_symmDiff_leproof · cited by 3
- iInf_iSup_eq_of_finiteproof · cited by 2
- biSup_constproof · cited by 2
- IntermediateField.normalClosure_of_normalproof · cited by 2
- Set.Finite.iSup_biInf_of_monotoneproof · cited by 2
- sup_iSupproof · cited by 2
- Set.Finite.biInf_iSup_eqproof · cited by 1
- Real.dimH_univ_piproof · cited by 1
- MeasureTheory.VectorMeasure.iSup_sum_finpartition_partsproof · cited by 1