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Proof step 10 from proof ls-add-01 (previous step)

⊦ i * 10 ^ abs(i2) < i1 * 10 ^ abs(j) + i0 * 10 ^ abs(i2) ↔ mkDecimal(i - i0, j) < mkDecimal(i1, i2)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ mkDecimal(i, j) < mkDecimal(i0, j0) ↔ i * 10 ^ abs(j0) < i0 * 10 ^ abs(j)
Proof step 12:
⊦ i * 10 ^ abs(i2) < i1 * 10 ^ abs(j) + i0 * 10 ^ abs(i2) ↔ (i - i0) * 10 ^ abs(i2) < i1 * 10 ^ abs(j)

Rule argument

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

Additional information

Used terms: i2, i1, j, i - i0