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Proof step 7 from proof maxScale-pot10-add (previous step)

0 ≤ j0, 0 ≤ j ⊦ i % 10 = 0, i0 % 10 = 0, (i + i0) % 10 = 0, maxScale((i * 10 ^ (j - min(j, j0)) + i0 * 10 ^ (j0 - min(j, j0))) * 10 ^ min(j, j0)) = min(j, j0), (i * 10 ^ (j - min(j, j0)) + i0 * 10 ^ (j0 - min(j, j0))) % 10 ≠ 0 ∧ 0 ≤ min(j, j0)

User applied rule cut formula

And obtained the following new goals

Proof step 8:
0 ≤ min(j, j0), 0 ≤ j0, 0 ≤ j ⊦ i % 10 = 0, i0 % 10 = 0, (i + i0) % 10 = 0, maxScale((i * 10 ^ (j - min(j, j0)) + i0 * 10 ^ (j0 - min(j, j0))) * 10 ^ min(j, j0)) = min(j, j0), (i * 10 ^ (j - min(j, j0)) + i0 * 10 ^ (j0 - min(j, j0))) % 10 ≠ 0 ∧ 0 ≤ min(j, j0)
Proof step 17:
0 ≤ j0, 0 ≤ j ⊦ 0 ≤ min(j, j0), i % 10 = 0, i0 % 10 = 0, (i + i0) % 10 = 0, maxScale((i * 10 ^ (j - min(j, j0)) + i0 * 10 ^ (j0 - min(j, j0))) * 10 ^ min(j, j0)) = min(j, j0), (i * 10 ^ (j - min(j, j0)) + i0 * 10 ^ (j0 - min(j, j0))) % 10 ≠ 0 ∧ 0 ≤ min(j, j0)

Rule argument

fma: 0 ≤ min(j, j0)

Additional information

Used formulas: 0 ≤ min(j, j0)