Theorems · Theorem · functional analysis
LinearIsometry.antilipschitz
∀ {R : Type u_1} {R₂ : Type u_2} {E : Type u_5} {E₂ : Type u_6} [inst : Semiring R] [inst_1 : Semiring R₂]
{σ₁₂ : R →+* R₂} [inst_2 : SeminormedAddCommGroup E] [inst_3 : SeminormedAddCommGroup E₂] [inst_4 : Module R E]
[inst_5 : Module R₂ E₂] (f : E →ₛₗᵢ[σ₁₂] E₂), AntilipschitzWith 1 ⇑f- Cited by
- 1 results in Mathlib
- Foundations
- Depth 157 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.
- DFunLike.coestatement · cited by 62,936
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- RingHomstatement and proof · cited by 10,189
- NNRealstatement · cited by 4,310
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- LinearIsometrystatement and proof · cited by 194
- AntilipschitzWithstatement · cited by 132
- LinearIsometry.isometryproof · cited by 24
- Isometry.antilipschitzproof · cited by 14
Cited by1
Results whose statement or proof uses this declaration.
- LinearIsometry.integral_comp_commproof · cited by 4