Theorems · Theorem · functional analysis
LinearIsometry.dist_map
∀ {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) (x y : E), dist (f x) (f y) = dist x y- Cited by
- 2 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
- Realstatement · cited by 25,697
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- RingHomstatement and proof · cited by 10,189
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Dist.diststatement · cited by 1,539
- LinearIsometrystatement and proof · cited by 194
- LinearIsometry.isometryproof · cited by 24
- Isometry.dist_eqproof · cited by 21
Cited by2
Results whose statement or proof uses this declaration.
- LinearIsometryEquiv.dist_mapproof · cited by 3
- dist_iteratedFDerivWithin_oneproof · cited by 0