Theorems · Theorem · convex and discrete geometry
sbtw_zero_one_iff
∀ {R : Type u_1} [inst : Ring R] [inst_1 : PartialOrder R] {x : R}, Sbtw R 0 x 1 ↔ x ∈ Set.Ioo 0 1- Defined in
- Mathlib.Analysis.Convex.Between
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 49 from the axioms · uses propext, Quot.sound
- Assumes
- RingPartialOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- LT.lt.leproof · cited by 2,189
- LT.lt.ne'proof · cited by 1,417
- Set.Ioostatement and proof · cited by 1,214
- LT.lt.neproof · cited by 872
- Sbtwstatement · cited by 122
- LE.le.lt_of_neproof · cited by 116
- Set.mem_Iccproof · cited by 46
- Set.mem_Iooproof · cited by 29
- wbtw_zero_one_iffproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- sbtw_one_zero_iffproof · cited by 1