AffineSubspace.SOppSide.trans
∀ {R : Type u_1} {V : Type u_2} {P : Type u_4} [inst : Field R] [inst_1 : LinearOrder R]
[inst_2 : IsStrictOrderedRing R] [inst_3 : AddCommGroup V] [inst_4 : Module R V] [inst_5 : AddTorsor V P]
{s : AffineSubspace R P} {x y z : P}, s.SOppSide x y → s.SOppSide y z → s.SSameSide x z- Defined in
- Mathlib.Analysis.Convex.Side
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 56 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
- LinearOrderstatement and proof · cited by 8,572
- Fieldstatement and proof · cited by 7,404
- IsStrictOrderedRingstatement and proof · cited by 2,490
- AddTorsorstatement and proof · cited by 1,657
- AffineSubspacestatement and proof · cited by 871
- AffineSubspace.SOppSidestatement and proof · cited by 56
- AffineSubspace.SSameSidestatement · cited by 55
- AffineSubspace.SOppSide.trans_wOppSideproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- EuclideanGeometry.angle_eq_pi_sub_angle_div_two_of_oangle_eq_of_sOppSideproof · cited by 1
- AffineSubspace.SOppSide.oangle_sign_eq_negproof · cited by 0