Theorems · Theorem · functional analysis
SameRay.norm_sub
∀ {E : Type u_1} [inst : SeminormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {x y : E},
SameRay ℝ x y → ‖x - y‖ = |‖x‖ - ‖y‖|- Defined in
- Mathlib.Analysis.Normed.Module.Ray
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- NormedSpacestatement and proof · cited by 12,499
- Norm.normstatement and proof · cited by 5,413
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- absstatement and proof · cited by 1,814
- norm_nonnegproof · cited by 725
- mul_nonnegproof · cited by 397
- abs_of_nonnegproof · cited by 279
- sub_mulproof · cited by 170
- sub_nonnegproof · cited by 167
- SameRaystatement and proof · cited by 149
- sub_smulproof · cited by 97
Cited by2
Results whose statement or proof uses this declaration.
- sameRay_iff_norm_subproof · cited by 2
- Complex.norm_sub_eqproof · cited by 0