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Theorems · Theorem · functional analysis

NormedAddGroupHom.Equalizer.lift_normNoninc

∀ {V : Type u_1} {W : Type u_2} {V₁ : Type u_3} [inst : SeminormedAddCommGroup V] [inst_1 : SeminormedAddCommGroup W]
  [inst_2 : SeminormedAddCommGroup V₁] {f g : NormedAddGroupHom V W} (φ : NormedAddGroupHom V₁ V)
  (h : f.comp φ = g.comp φ), φ.NormNoninc → (NormedAddGroupHom.Equalizer.lift φ h).NormNoninc

The lifting of a norm nonincreasing morphism is norm nonincreasing.

Defined in
Mathlib.Analysis.Normed.Group.Hom
Cited by
1 results in Mathlib
Foundations
Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SeminormedAddCommGroupSeminormedAddCommGroupSeminormedAddCommGroup
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Around this declaration

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NormedAddGroupHom.Equalizer.map_normNoninc · cited by 0Equalizer.map_normNonincAddSubgroup · cited by 3232AddSubgroupSeminormedAddCommGroup · cited by 2671SeminormedAddCommGroupNormedAddGroupHom · cited by 216NormedAddGroupHomNormedAddGroupHom.NormNoninc · cited by 41NormedAddGroupHom.NormNon…NormedAddGroupHom.comp · cited by 39NormedAddGroupHom.compNormedAddGroupHom.equalizer · cited by 14NormedAddGroupHom.equaliz…NormedAddGroupHom.Equalizer.lift · cited by 6Equalizer.liftEqualizer.lift_normNonincCITED BYCITES

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