Theorems · Definition · functional analysis

AlgebraNorm.casesOn

{R : Type u_1} →
  [inst : SeminormedCommRing R] →
    {S : Type u_2} →
      [inst_1 : Ring S] →
        [inst_2 : Algebra R S] →
          {motive : AlgebraNorm R S → Sort u} →
            (t : AlgebraNorm R S) →
              ((toRingNorm : RingNorm S) →
                  (smul' : ∀ (a : R) (x : S), toRingNorm.toFun (a • x) = ‖a‖ * toRingNorm.toFun x) →
                    motive { toRingNorm := toRingNorm, smul' := smul' }) →
                motive t

Defined in

Mathlib.Analysis.Normed.Unbundled.AlgebraNorm

Cited by

0 results in Mathlib

Foundations

Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SeminormedCommRingRingAlgebra