Theorems · Theorem · functional analysis
sameRay_iff_norm_sub
∀ {E : Type u_2} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [StrictConvexSpace ℝ E] {x y : E},
SameRay ℝ x y ↔ ‖x - y‖ = |‖x‖ - ‖y‖|- Cited by
- 2 results in Mathlib
- Foundations
- Depth 168 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.
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Norm.normstatement and proof · cited by 5,413
- absstatement and proof · cited by 1,814
- LT.lt.ne'proof · cited by 1,417
- SameRaystatement and proof · cited by 149
- StrictConvexSpacestatement and proof · cited by 57
- SameRay.norm_subproof · cited by 2
- abs_lt_norm_sub_of_not_sameRayproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Complex.norm_sub_eq_iffproof · cited by 0
- not_sameRay_iff_abs_lt_norm_subproof · cited by 0