Theorems · Theorem · functional analysis
not_sameRay_iff_of_norm_eq
∀ {F : Type u_2} [inst : NormedAddCommGroup F] [inst_1 : NormedSpace ℝ F] {x y : F},
‖x‖ = ‖y‖ → (¬SameRay ℝ x y ↔ x ≠ y)- Defined in
- Mathlib.Analysis.Normed.Module.Ray
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Iff.notproof · cited by 489
- SameRaystatement · cited by 149
- sameRay_iff_of_norm_eqproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- norm_midpoint_lt_iffproof · cited by 0