Theorems · Theorem · linear algebra
SameRay.exists_pos_right
∀ {R : Type u_1} [inst : Field R] [inst_1 : LinearOrder R] [inst_2 : IsStrictOrderedRing R] {M : Type u_2}
[inst_3 : AddCommGroup M] [inst_4 : Module R M] {x y : M}, SameRay R x y → x ≠ 0 → y ≠ 0 → ∃ r, 0 < r ∧ x = r • y- Defined in
- Mathlib.LinearAlgebra.Ray
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 47 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- SameRaystatement and proof · cited by 149
- SameRay.symmproof · cited by 9
- SameRay.exists_pos_leftproof · cited by 5
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