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Proof step 7 from proof ls-add-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ 0 ≤ j0 → mkDecimal(i, j) = mkDecimal(i * 10 ^ j0, abs(j) + j0)
Proof step 9:
0 ≤ abs(i2) ⊦ mkDecimal(i * 10 ^ abs(i2), abs(abs(j)) + abs(i2)) < mkDecimal(i1 * 10 ^ abs(j) + i0 * 10 ^ abs(i2), abs(i2) + abs(j)) ↔ mkDecimal(i - i0, j) < mkDecimal(i1, i2)

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(i2), abs(j), i] flags: rewrite

Additional information

Used simplifier rules: ls-not: ⊦ ¬ dec < dec0 ↔ dec0 ≤ dec;%abs-03: ⊦ 0 ≤ abs(i); from specification int-abs Used terms: abs(i2), abs(j), i