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Proof step 3 from proof ls-add-01 (previous step)

⊦ mkDecimal(i, j) < mkDecimal(i1, i2) + mkDecimal(i0, j) ↔ mkDecimal(i - i0, j) < mkDecimal(i1, i2)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ mkDecimal(i, j) + mkDecimal(i0, j0) = mkDecimal(i * 10 ^ abs(j0) + i0 * 10 ^ abs(j), abs(j) + abs(j0))
Proof step 5:
⊦ mkDecimal(i, j) < mkDecimal(i1 * 10 ^ abs(j) + i0 * 10 ^ abs(i2), abs(i2) + abs(j)) ↔ mkDecimal(i - i0, j) < mkDecimal(i1, i2)

Rule argument

spec: inst: name: add-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] → [j, i0, i2, i1] flags: rewrite, current

Additional information

Used terms: j, i0, i2, i1