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Proof step 10 from proof add-scale-neq (previous step)

maxScale(dec_i.int * 10 ^ dec_j.scale + dec_j.int * 10 ^ dec_i.scale) ≤ abs(dec_i.scale + dec_j.scale) ⊦ dec_i.scale = dec_j.scale, abs(dec_i.scale + dec_j.scale) = max(dec_i.scale, dec_j.scale) + maxScale(dec_i.int * 10 ^ dec_j.scale + dec_j.int * 10 ^ dec_i.scale)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ 0 ≤ j ∧ 0 ≤ j0 ∧ i % 10 ≠ 0 ∧ i0 % 10 ≠ 0 ∧ (i + i0) % 10 ≠ 0 → maxScale(i * 10 ^ j + i0 * 10 ^ j0) = min(j, j0)
Proof step 12:
¬(0 ≤ dec_j.scale ∧ 0 ≤ dec_i.scale ∧ dec_i.int % 10 ≠ 0 ∧ dec_j.int % 10 ≠ 0 ∧ (dec_i.int + dec_j.int) % 10 ≠ 0), maxScale(dec_i.int * 10 ^ dec_j.scale + dec_j.int * 10 ^ dec_i.scale) ≤ abs(dec_i.scale + dec_j.scale) ⊦ dec_i.scale = dec_j.scale, abs(dec_i.scale + dec_j.scale) = max(dec_i.scale, dec_j.scale) + maxScale(dec_i.int * 10 ^ dec_j.scale + dec_j.int * 10 ^ dec_i.scale)
Proof step 73:
0 ≤ dec_j.scale ∧ 0 ≤ dec_i.scale ∧ dec_i.int % 10 ≠ 0 ∧ dec_j.int % 10 ≠ 0 ∧ (dec_i.int + dec_j.int) % 10 ≠ 0, min(dec_j.scale, dec_i.scale) ≤ abs(dec_i.scale + dec_j.scale) ⊦ dec_i.scale = dec_j.scale, abs(dec_i.scale + dec_j.scale) = max(dec_i.scale, dec_j.scale) + min(dec_j.scale, dec_i.scale)

Rule argument

spec: decimal inst: name: maxScale-pot10-add seq: ⊦ 0 ≤ j ∧ 0 ≤ j0 ∧ i % 10 ≠ 0 ∧ i0 % 10 ≠ 0 ∧ (i + i0) % 10 ≠ 0 → maxScale(i * 10 ^ j + i0 * 10 ^ j0) = min(j, j0) subst: [j0, i0, j, i] → [dec_i.scale, dec_j.int, dec_j.scale, dec_i.int] flags: rewrite

Additional information

Used terms: dec_i.scale, dec_j.int, dec_j.scale, dec_i.int