Theorems · Theorem · convex and discrete geometry
sbtw_const_vsub_iff
∀ {R : Type u_1} {V : Type u_2} {P : Type u_4} [inst : Ring R] [inst_1 : PartialOrder R] [inst_2 : AddCommGroup V]
[inst_3 : Module R V] [inst_4 : AddTorsor V P] {x y z : P} (p : P), Sbtw R (p -ᵥ x) (p -ᵥ y) (p -ᵥ z) ↔ Sbtw R x y z- Defined in
- Mathlib.Analysis.Convex.Between
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Ringstatement and proof · cited by 7,463
- PartialOrderstatement and proof · cited by 6,410
- AddTorsorstatement and proof · cited by 1,657
- VSub.vsubstatement and proof · cited by 817
- Wbtwproof · cited by 165
- Sbtwstatement and proof · cited by 122
- wbtw_const_vsub_iffproof · cited by 3
- vsub_right_injectiveproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- sbtw_const_sub_iffproof · cited by 1
- Sbtw.const_vsubproof · cited by 0