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Proof step 21 from proof mult-dist (previous step)

0 ≤ abs(i0) ⊦ mkDecimal((i * (i1 * 10 ^ abs(i4) + i3 * 10 ^ abs(i2))) * 10 ^ abs(i0), abs(abs(i0) + abs(i2) + abs(i4)) + abs(i0)) = mkDecimal(i * i1 * 10 ^ (abs(i0) + abs(i4)) + i * i3 * 10 ^ (abs(i0) + abs(i2)), 2 * abs(i0) + abs(i2) + abs(i4))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 22:
⊦ (i * (i1 * 10 ^ abs(i4) + i3 * 10 ^ abs(i2))) * 10 ^ abs(i0) = i * i1 * 10 ^ (abs(i0) + abs(i4)) + i * i3 * 10 ^ (abs(i0) + abs(i2))

Rule argument

Additional information

Used simplifier rules: abs-03: ⊦ 0 ≤ abs(i); from specification int-abs%eq-same: ⊦ mkDecimal(i, j) = mkDecimal(i0, j) ↔ i = i0; from specification decimal%add-mult-two: ⊦ i + i = 2 * i; from specification int-mult%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%abs-20: ⊦ abs(abs(i) + abs(i0) + abs(i1)) = abs(i) + abs(i0) + abs(i1); from specification int-abs