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Proof step 14 from proof less-trans (previous step)

mkDecimal(i1, abs(i2)) < mkDecimal(i3, abs(i4)), mkDecimal(i, abs(i0)) < mkDecimal(i1, abs(i2)) ⊦ mkDecimal(i, abs(i0)) < mkDecimal(i3, abs(i4))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ 0 ≤ j0 → mkDecimal(i, j) = mkDecimal(i * 10 ^ j0, abs(j) + j0)
Proof step 16:
0 ≤ abs(i0) + abs(i4), mkDecimal(i1 * 10 ^ (abs(i0) + abs(i4)), abs(abs(i2)) + abs(i0) + abs(i4)) < mkDecimal(i3, abs(i4)), mkDecimal(i, abs(i0)) < mkDecimal(i1 * 10 ^ (abs(i0) + abs(i4)), abs(abs(i2)) + abs(i0) + abs(i4)) ⊦ mkDecimal(i, abs(i0)) < mkDecimal(i3, 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(i4), abs(i2), i1] flags: rewrite

Additional information

Used simplifier rules: lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%abs-add-pos: ⊦ ¬ abs(i) + abs(j) < 0; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: abs(i0) + abs(i4), abs(i2), i1