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Proof step 23 from proof add-scale-neq (previous step)

(dec_i.int + dec_j.int) % 10 = 0, 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))) * 10 ^ min(dec_j.scale, dec_i.scale)) ≤ dec_i.scale + dec_j.scale, 0 ≤ dec_i.scale, 0 ≤ dec_j.scale ⊦ dec_i.scale = dec_j.scale, dec_i.scale + dec_j.scale = max(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))) * 10 ^ min(dec_j.scale, dec_i.scale)), dec_i.int % 10 = 0, dec_j.int % 10 = 0, 0 ≤ min(dec_j.scale, dec_i.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 cut formula

And obtained the following new goals

Proof step 24:
0 ≤ min(dec_j.scale, dec_i.scale), (dec_i.int + dec_j.int) % 10 = 0, 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))) * 10 ^ min(dec_j.scale, dec_i.scale)) ≤ dec_i.scale + dec_j.scale, 0 ≤ dec_i.scale, 0 ≤ dec_j.scale ⊦ dec_i.scale = dec_j.scale, dec_i.scale + dec_j.scale = max(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))) * 10 ^ min(dec_j.scale, dec_i.scale)), dec_i.int % 10 = 0, dec_j.int % 10 = 0, 0 ≤ min(dec_j.scale, dec_i.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 43:
(dec_i.int + dec_j.int) % 10 = 0, 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))) * 10 ^ min(dec_j.scale, dec_i.scale)) ≤ dec_i.scale + dec_j.scale, 0 ≤ dec_i.scale, 0 ≤ dec_j.scale ⊦ 0 ≤ min(dec_j.scale, dec_i.scale), dec_i.scale = dec_j.scale, dec_i.scale + dec_j.scale = max(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))) * 10 ^ min(dec_j.scale, dec_i.scale)), dec_i.int % 10 = 0, dec_j.int % 10 = 0, 0 ≤ min(dec_j.scale, dec_i.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

fma: 0 ≤ min(dec_j.scale, dec_i.scale)

Additional information

Used formulas: 0 ≤ min(dec_j.scale, dec_i.scale)