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Theorems · Theorem · functional analysis

NormedAddGroupHom.comp_apply

∀ {V₁ : Type u_2} {V₂ : Type u_3} {V₃ : Type u_4} [inst : SeminormedAddCommGroup V₁]
  [inst_1 : SeminormedAddCommGroup V₂] [inst_2 : SeminormedAddCommGroup V₃] (g : NormedAddGroupHom V₂ V₃)
  (f : NormedAddGroupHom V₁ V₂) (a : V₁), (g.comp f) a = g (f a)
Defined in
Mathlib.Analysis.Normed.Group.Hom
Cited by
5 results in Mathlib
Foundations
Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SeminormedAddCommGroupSeminormedAddCommGroupSeminormedAddCommGroup
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

SemiNormedGrp₁.comp_apply · cited by 3SemiNormedGrp₁.comp_applySemiNormedGrp.comp_apply · cited by 1SemiNormedGrp.comp_applyNormedAddGroupHom.ker_le_ker_completion · cited by 1NormedAddGroupHom.ker_le_…NormedAddGroupHom.completion_toCompl · cited by 0NormedAddGroupHom.complet…NormedAddGroupHom.Equalizer.comp_ι_eq · cited by 0Equalizer.comp_ι_eqDFunLike.coe · cited by 62936DFunLike.coeSeminormedAddCommGroup · cited by 2671SeminormedAddCommGroupNormedAddGroupHom · cited by 216NormedAddGroupHomNormedAddGroupHom.comp · cited by 39NormedAddGroupHom.compNormedAddGroupHom.comp_applyCITED BYCITES

Cites4

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Cited by5

Results whose statement or proof uses this declaration.