Theorems · Theorem · functional analysis
LinearIsometry.coe_toLinearMap
∀ {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), ⇑f.toLinearMap = ⇑f- Cited by
- 2 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- LinearMapstatement · cited by 10,215
- RingHomstatement and proof · cited by 10,189
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- LinearIsometrystatement and proof · cited by 194
- LinearIsometry.toLinearMapstatement · cited by 55
Cited by2
Results whose statement or proof uses this declaration.
- EuclideanGeometry.orthogonalProjection_mapproof · cited by 3
- IsHilbertSum.mkproof · cited by 2