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Proof step 7 from proof sub-add (previous step)

⊦ mkDecimal(i * 10 ^ abs(i2) + i1 * 10 ^ abs(i0), abs(i0) + abs(i2)) - mkDecimal(i1, i2) = mkDecimal(i, i0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ mkDecimal(i, j) - mkDecimal(i0, j0) = mkDecimal(i * 10 ^ abs(j0) - i0 * 10 ^ abs(j), abs(j) + abs(j0))
Proof step 9:
⊦ mkDecimal((i * 10 ^ abs(i2) + i1 * 10 ^ abs(i0)) * 10 ^ abs(i2) - i1 * 10 ^ abs(abs(i0) + abs(i2)), abs(abs(i0) + abs(i2)) + abs(i2)) = mkDecimal(i, i0)

Rule argument

spec: inst: name: sub-def-any seq: ⊦ mkDecimal(i, j) - mkDecimal(i0, j0) = mkDecimal (i * 10 ^ abs(j0) - i0 * 10 ^ abs(j), abs(j) + abs(j0)) subst: [j0, i0, j, i] → [i2, i1, abs(i0) + abs(i2), i * 10 ^ abs(i2) + i1 * 10 ^ abs(i0)] flags: rewrite, current

Additional information

Used terms: i2, i1, abs(i0) + abs(i2), i * 10 ^ abs(i2) + i1 * 10 ^ abs(i0)