Theorems · Theorem · order theory
csInf_mem
∀ {α : Type u_1} [inst : ConditionallyCompleteLinearOrder α] {s : Set α} [WellFoundedLT α], s.Nonempty → sInf s ∈ s- Cited by
- 19 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Setstatement and proof · cited by 53,352
- Set.Nonemptystatement and proof · cited by 2,627
- InfSet.sInfstatement · cited by 935
- ConditionallyCompleteLinearOrderstatement and proof · cited by 542
- WellFoundedLTstatement and proof · cited by 491
- isLeast_csInfproof · cited by 4
Cited by19
Results whose statement or proof uses this declaration.
- Submodule.exists_span_set_card_eq_spanRankproof · cited by 11
- Submodule.spanRank_finite_iff_fgproof · cited by 5
- ciInf_memproof · cited by 5
- ENat.exists_eq_iInfproof · cited by 4
- Ordinal.range_enumOrdproof · cited by 4
- SimpleGraph.Reachable.exists_walk_length_eq_edistproof · cited by 3
- MeasureTheory.stoppedValue_hittingBtwn_memproof · cited by 3
- Ordinal.lt_veblen_invVeblen₁proof · cited by 3
- MeasureTheory.hittingBtwn_mem_setproof · cited by 2
- CategoryTheory.projectiveDimension_lt_iffproof · cited by 2
- Ordinal.exists_lsub_cofproof · cited by 2
- CategoryTheory.injectiveDimension_lt_iffproof · cited by 2