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Proof step 20 from proof less-trans (previous step)

mkDecimal(i, abs(i0)) < mkDecimal(i1 * 10 ^ (abs(i0) + abs(i4)), abs(i2) + abs(i0) + abs(i4)), 0 ≤ abs(i0) + abs(i4), i1 * 10 ^ (abs(i0) + abs(i4)) < i3 * 10 ^ (abs(i0) + abs(i2)), 0 ≤ abs(i0) + abs(i2) ⊦ mkDecimal(i, abs(i0)) < mkDecimal(i3 * 10 ^ (abs(i0) + abs(i2)), abs(i4) + abs(i0) + abs(i2))

User applied rule insert rewrite lemma

And obtained the following new goals

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(i4) + abs(i2), abs(i0), i] flags: rewrite

Additional information

Used simplifier rules: less-same: ⊦ mkDecimal(i, j) < mkDecimal(i0, j) ↔ i < i0;%abs-01: ⊦ abs(abs(i)) = abs(i); 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%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%abs-add-pos: ⊦ ¬ abs(i) + abs(j) < 0; from specification int-abs Used terms: abs(i4) + abs(i2), abs(i0), i