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Proof step 19 from proof mult-dist (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ 0 ≤ j0 → mkDecimal(i, j) = mkDecimal(i * 10 ^ j0, abs(j) + j0)
Proof step 21:
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))

Rule argument

spec: decimal inst: name: mkDecimal-enlarge seq: ⊦ 0 ≤ j0 → mkDecimal(i, j) = mkDecimal(i * 10 ^ j0, abs(j) + j0) subst: [j0, j, i] → [abs(i0), abs(i0) + abs(i2) + abs(i4), i * (i1 * 10 ^ abs(i4) + i3 * 10 ^ abs(i2))] flags: rewrite

Additional information

Used simplifier rules: abs-03: ⊦ 0 ≤ abs(i); from specification int-abs Used terms: abs(i0), abs(i0) + abs(i2) + abs(i4), i * (i1 * 10 ^ abs(i4) + i3 * 10 ^ abs(i2))