Theorems · Theorem · order theory
Set.Nonempty.csSup_mem
∀ {α : Type u_2} [inst : ConditionallyCompleteLinearOrder α] {s : Set α}, s.Nonempty → s.Finite → sSup s ∈ s- Cited by
- 11 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Finsetproof · cited by 13,712
- SetLike.coeproof · cited by 8,199
- Set.Nonemptystatement and proof · cited by 2,627
- Set.Finitestatement and proof · cited by 1,814
- SupSet.sSupstatement · cited by 954
- ConditionallyCompleteLinearOrderstatement and proof · cited by 542
- Finset.Nonempty.csSup_memproof · cited by 2
Cited by11
Results whose statement or proof uses this declaration.
- exists_eq_ciSup_of_finiteproof · cited by 8
- Nat.sSup_memproof · cited by 5
- sSup_ne_of_notMemproof · cited by 3
- MeasureTheory.upperCrossingTime_lt_of_le_upcrossingsBeforeproof · cited by 3
- Set.Nonempty.csInf_memproof · cited by 3
- Set.Nonempty.ordConnected_iff_of_bddproof · cited by 3
- Set.Finite.csSup_lt_iffproof · cited by 2
- AddMonoid.exists_addOrderOf_eq_exponentproof · cited by 1
- ENat.sSup_mem_of_nonempty_of_lt_topproof · cited by 1
- Monoid.exists_orderOf_eq_exponentproof · cited by 1
- Set.Finite.map_sSup_of_monotoneproof · cited by 0