Theorems · Theorem · functional analysis
SeminormFamily.comp_smul_nnreal
∀ {𝕜 : Type u_2} {𝕜₂ : Type u_3} {E : Type u_6} {F : Type u_7} {ι : Type u_9} [inst : NormedField 𝕜]
[inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E] [inst_3 : NormedField 𝕜₂] [inst_4 : AddCommGroup F]
[inst_5 : Module 𝕜₂ F] {σ₁₂ : 𝕜 →+* 𝕜₂} [inst_6 : RingHomIsometric σ₁₂] (q : SeminormFamily 𝕜₂ F ι) (c : NNReal)
(f : E →ₛₗ[σ₁₂] F), c • q.comp f = (c • q).comp f- Cited by
- 0 results in Mathlib
- Foundations
- Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement · cited by 25,697
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement and proof · cited by 10,215
- RingHomstatement and proof · cited by 10,189
- NNRealstatement and proof · cited by 4,310
- NormedFieldstatement and proof · cited by 1,084
- RingHomIsometricstatement and proof · cited by 282
- Seminormstatement · cited by 272
- smul_applyproof · cited by 229
- SeminormFamilystatement and proof · cited by 68
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