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Proof step 13 from proof mod-nls-04 (previous step)

i0 < 0, i % j < i0, abs(i % j) < j, 0 < j, i0 + j ≤ 0 ⊦ i0 + j = 1

User applied rule cut formula

And obtained the following new goals

Proof step 14:
0 < j, abs(i % j) < j, i % j < i0, i0 < 0, abs(i % j) < abs(i0), i0 + j ≤ 0 ⊦ i0 + j = 1

Rule argument

fma: abs(i % j) < abs(i0)

Additional information

Used simplifier rules: ⊦ i < 0 → abs(i) = ~ i; (s)% ⊦ i < ~ j ↔ i + j < 0; (s)% ⊦ i < j ↔ ¬ j ≤ i; (ss)%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs% ⊦ i < 0 ∧ 0 ≤ j → i < j; (s)% ⊦ i + j ≤ i0 + j ↔ i ≤ i0; (s)% ⊦ i < j → (j ≤ i ↔ false); (as)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used formulas: abs(i % j) < abs(i0)