Theorems · Theorem · complex analysis
Complex.restrictScalars_toSpanSingleton
∀ (x : ℂ), ContinuousLinearMap.restrictScalars ℝ (ContinuousLinearMap.toSpanSingleton ℂ x) = x • 1
- Defined in
- Mathlib.Analysis.Complex.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Realstatement · cited by 25,697
- RingHom.idstatement · cited by 18,349
- Complexstatement and proof · cited by 5,565
- ContinuousLinearMapstatement · cited by 5,352
- mul_commproof · cited by 2,262
- ContinuousLinearMap.extproof · cited by 320
- ContinuousLinearMap.toSpanSingletonstatement · cited by 133
- ContinuousLinearMap.restrictScalarsstatement · cited by 61
Cited by3
Results whose statement or proof uses this declaration.
- HasStrictDerivAt.complexToReal_fderivproof · cited by 2
- HasDerivAt.complexToReal_fderivproof · cited by 0
- HasDerivWithinAt.complexToReal_fderivproof · cited by 0