Theorems · Theorem · complex analysis
ContinuousLinearMap.restrictScalars.congr_simp
∀ {A : Type u_1} {M₁ : Type u_2} {M₂ : Type u_3} (R : Type u_4) [inst : Semiring A] [inst_1 : Semiring R]
[inst_2 : AddCommMonoid M₁] [inst_3 : Module A M₁] [inst_4 : Module R M₁] [inst_5 : TopologicalSpace M₁]
[inst_6 : AddCommMonoid M₂] [inst_7 : Module A M₂] [inst_8 : Module R M₂] [inst_9 : TopologicalSpace M₂]
[inst_10 : LinearMap.CompatibleSMul M₁ M₂ R A] (f f_1 : M₁ →L[A] M₂),
f = f_1 → ContinuousLinearMap.restrictScalars R f = ContinuousLinearMap.restrictScalars R f_1- Defined in
- Mathlib.Analysis.Complex.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 26 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.
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- ContinuousLinearMapstatement and proof · cited by 5,352
- LinearMap.CompatibleSMulstatement and proof · cited by 86
- ContinuousLinearMap.restrictScalarsstatement and proof · cited by 61
Cited by5
Results whose statement or proof uses this declaration.
- UpperHalfPlane.smulFDeriv_J_mulproof · cited by 1
- isConformalMap_iff_is_complex_or_conj_linearproof · cited by 1
- UpperHalfPlane.det_smulFDerivproof · cited by 0
- Convex.exists_forall_hasDerivWithinAtproof · cited by 0
- UpperHalfPlane.hasStrictFDerivAt_smulproof · cited by 0