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Proof step 2 from proof modneqp (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 3:
i * i0 + j0 = i1 * j + j1, j1 < j, j0 < j, i0 ≤ j, i < i1, 0 ≤ j1, 0 ≤ j0, 0 < j, 0 ≤ i0, 0 ≤ j, 0 ≤ i, 0 < i1 ⊦ i * i0 + j0 < i1 * j + j1

Rule argument

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

Additional information

Used simplifier rules: lf-02: ⊦ i < j ∧ j = i0 → i < i0; (forward) from specification int-basic1%ls-01: ⊦ i + j < i + i0 ↔ j < i0; from specification int-basic2%irref: ⊦ ¬ i < i; from specification int-basic1%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used formulas: i * i0 + j0 < i1 * j + j1