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Step * of Lemma q-linear-sum

∀[X,Y:ℕ ⟶ ℚ]. ∀[k:ℕ]. ∀[y:ℚ List].
  q-linear(k;j.X[j] + Y[j];y) = (q-linear(k;j.X[j];y) + q-linear(k;j.Y[j];y)) ∈ ℚ supposing k ≤ ||y||
BY
{ xxx(InductionOnNat
      THEN Auto
      THEN Try ((RWO "q-linear-base" 0 THEN Auto))
      THEN RWO "q-linear-unroll" 0
      THEN Auto
      THEN ((RW (SweepDnC (HypC 5)) 0) THENA Auto)
      THEN QNorm 0)xxx }

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Latex:

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Latex:
\mforall{}[X,Y:\mBbbN{}  {}\mrightarrow{}  \mBbbQ{}].  \mforall{}[k:\mBbbN{}].  \mforall{}[y:\mBbbQ{}  List].
    q-linear(k;j.X[j]  +  Y[j];y)  =  (q-linear(k;j.X[j];y)  +  q-linear(k;j.Y[j];y))  supposing  k  \mleq{}  ||y||


By

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Latex:
xxx(InductionOnNat
        THEN  Auto
        THEN  Try  ((RWO  "q-linear-base"  0  THEN  Auto))
        THEN  RWO  "q-linear-unroll"  0
        THEN  Auto
        THEN  ((RW  (SweepDnC  (HypC  5))  0)  THENA  Auto)
        THEN  QNorm  0)xxx

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