Theorems · Theorem · general topology
Isometry.norm_map_of_map_one
∀ {E : Type u_2} {F : Type u_3} [inst : SeminormedGroup E] [inst_1 : SeminormedGroup F] {f : E → F},
Isometry f → f 1 = 1 → ∀ (x : E), ‖f x‖ = ‖x‖- Defined in
- Mathlib.Analysis.Normed.Group.Uniform
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 152 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
- Norm.normstatement and proof · cited by 5,413
- Dist.distproof · cited by 1,539
- SeminormedGroupstatement and proof · cited by 250
- Isometrystatement and proof · cited by 230
- Isometry.dist_eqproof · cited by 21
- dist_one_rightproof · cited by 20
Cited by2
Results whose statement or proof uses this declaration.
- norm_map'proof · cited by 1
- Isometry.nnnorm_map_of_map_oneproof · cited by 0