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Proof step 14 from proof mod-pred-neg (previous step)

i0 * j + j0 = (i2 * j + j1) + 1, i0 < j + j0, i2 < j + j0, j1 < j + j0, 0 < j + j0, abs(j1) < j, j0 < j, i0 < j, 0 < j, abs(j0) < j, i2 * j + j1 < ~1, i2 < j, j1 < j, i2 * j + j1 < 0, j0 ≤ 0, i0 ≤ 0, i2 ≤ 0, j1 ≤ 0 ⊦ 1 = j0 + j, j0 = j1 + 1, 0 ≤ j + j1 ∧ j1 < 0

User applied rule cut formula

And obtained the following new goals

Proof step 15:
i0 * j + j0 = (i2 * j + j1) + 1, j1 = 0, i2 * j + j1 < 0, j1 < j, i2 < j, i2 * j + j1 < ~1, abs(j0) < j, 0 < j, i0 < j, j0 < j, abs(j1) < j, 0 < j + j0, j1 < j + j0, i2 < j + j0, i0 < j + j0, j1 ≤ 0, i2 ≤ 0, i0 ≤ 0, j0 ≤ 0 ⊦ 1 = j0 + j, j0 = j1 + 1, 0 ≤ j + j1 ∧ j1 < 0

Rule argument

fma: j1 = 0

Additional information

Used simplifier rules: ⊦ i ≠ j → (i ≤ j ↔ i < j); (s)% ⊦ i < 0 → abs(i) = ~ i; (s)% ⊦ ~ i < j ↔ 0 < j + i; (s)% ⊦ i < 0 ∧ 0 ≤ j → i < j; (s)% ⊦ i ≤ j ↔ ¬ j < i; (ss)% ⊦ i < j → ¬ j < i; (s) Used formulas: j1 = 0