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Proof step 3 from proof modneqp (previous step)

i * i0 + j0 = i1 * j + j1, j1 < j, j0 < j, i < i1, 0 < j, 0 < i1, 0 ≤ j1, 0 ≤ j0, 0 ≤ i0, i0 ≤ j, 0 ≤ i, 0 ≤ j ⊦

User applied rule cut formula

And obtained the following new goals

Proof step 4:
i * i0 + j0 = i1 * j + j1, 0 < i1, 0 < j, i < i1, j0 < j, j1 < j, 0 ≤ j, 0 ≤ i, i0 ≤ j, 0 ≤ i0, 0 ≤ j0, 0 ≤ j1 ⊦ i * i0 + j0 < i1 * j + j1

Rule argument

fma: i * i0 + j0 < i1 * j + j1

Additional information

Used simplifier rules: lf-03: ⊦ i < j ∧ i = i0 → i0 < j; (forward) from specification int-basic1%lf-02: ⊦ i < j ∧ j = i0 → i < i0; (forward) from specification int-basic1% ⊦ i < j → ¬ j < i; (s) Used formulas: i * i0 + j0 < i1 * j + j1