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Theorems · Theorem · convex and discrete geometry

Sbtw.ne_left

∀ {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}, Sbtw R x y z → y ≠ x
Defined in
Mathlib.Analysis.Convex.Between
Cited by
8 results in Mathlib
Foundations
Depth 48 from the axioms · uses propext, Quot.sound
Assumes
RingPartialOrderAddCommGroupModuleAddTorsor

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.

  • 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
  • Sbtwstatement and proof · cited by 122

Cited by8

Results whose statement or proof uses this declaration.