Theorems · Theorem · convex and discrete geometry
sbtw_one_zero_iff
∀ {R : Type u_1} [inst : Ring R] [inst_1 : PartialOrder R] [IsOrderedRing R] {x : R}, Sbtw R 1 x 0 ↔ x ∈ Set.Ioo 0 1- Defined in
- Mathlib.Analysis.Convex.Between
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 52 from the axioms · uses propext, 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 · cited by 53,352
- Ringstatement and proof · cited by 7,463
- PartialOrderstatement and proof · cited by 6,410
- Set.Ioostatement and proof · cited by 1,214
- IsOrderedRingstatement and proof · cited by 777
- Sbtwstatement · cited by 122
- sbtw_commproof · cited by 5
- sbtw_zero_one_iffproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- sbtw_of_sbtw_of_sbtw_of_mem_affineSpan_pairproof · cited by 0