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Proof step 88 from proof add-scale-neq (previous step)

dec_i.scale + dec_j.scale < maxScale(dec_i.int * 10 ^ (dec_j.scale - min(dec_j.scale, dec_i.scale)) + dec_j.int * 10 ^ (dec_i.scale - min(dec_j.scale, dec_i.scale))) + min(dec_j.scale, dec_i.scale), 0 ≤ dec_j.scale, 0 ≤ dec_i.scale, 0 ≤ min(dec_j.scale, dec_i.scale) ⊦ dec_i.scale = dec_j.scale, 0 = max(dec_i.scale, dec_j.scale), dec_i.int * 10 ^ (dec_j.scale - min(dec_j.scale, dec_i.scale)) + dec_j.int * 10 ^ (dec_i.scale - min(dec_j.scale, dec_i.scale)) = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 89:
⊦ i % 10 ≠ 0 ∧ i ≠ 0 → maxScale(i) = 0
Proof step 90:
¬ ( (dec_i.int * 10 ^ (dec_j.scale - min(dec_j.scale, dec_i.scale)) + dec_j.int * 10 ^ (dec_i.scale - min(dec_j.scale, dec_i.scale))) % 10 ≠ 0 ∧ dec_i.int * 10 ^ (dec_j.scale - min(dec_j.scale, dec_i.scale)) + dec_j.int * 10 ^ (dec_i.scale - min(dec_j.scale, dec_i.scale)) ≠ 0), dec_i.scale + dec_j.scale < maxScale(dec_i.int * 10 ^ (dec_j.scale - min(dec_j.scale, dec_i.scale)) + dec_j.int * 10 ^ (dec_i.scale - min(dec_j.scale, dec_i.scale))) + min(dec_j.scale, dec_i.scale), 0 ≤ dec_j.scale, 0 ≤ dec_i.scale, 0 ≤ min(dec_j.scale, dec_i.scale) ⊦ dec_i.scale = dec_j.scale, 0 = max(dec_i.scale, dec_j.scale), dec_i.int * 10 ^ (dec_j.scale - min(dec_j.scale, dec_i.scale)) + dec_j.int * 10 ^ (dec_i.scale - min(dec_j.scale, dec_i.scale)) = 0
Proof step 99:
(dec_i.int * 10 ^ (dec_j.scale - min(dec_j.scale, dec_i.scale)) + dec_j.int * 10 ^ (dec_i.scale - min(dec_j.scale, dec_i.scale))) % 10 ≠ 0 ∧ dec_i.int * 10 ^ (dec_j.scale - min(dec_j.scale, dec_i.scale)) + dec_j.int * 10 ^ (dec_i.scale - min(dec_j.scale, dec_i.scale)) ≠ 0, dec_i.scale + dec_j.scale < 0 + min(dec_j.scale, dec_i.scale), 0 ≤ dec_j.scale, 0 ≤ dec_i.scale, 0 ≤ min(dec_j.scale, dec_i.scale) ⊦ dec_i.scale = dec_j.scale, 0 = max(dec_i.scale, dec_j.scale), dec_i.int * 10 ^ (dec_j.scale - min(dec_j.scale, dec_i.scale)) + dec_j.int * 10 ^ (dec_i.scale - min(dec_j.scale, dec_i.scale)) = 0

Rule argument

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

Additional information

Used terms: dec_i.int * 10 ^ (dec_j.scale - min(dec_j.scale, dec_i.scale)) + dec_j.int * 10 ^ (dec_i.scale - min(dec_j.scale, dec_i.scale))