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Proof step 5 from proof modlep-03 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
0 ≤ i1 + j1, abs(j1) < abs(i1), i1 + j1 < abs(i1), j * i + i1 ≤ j * i0, 0 < j, j ≤ abs(i1), i0 < i, abs(j1) < j, i1 + j1 < j ⊦ i1 = 0

Rule argument

Additional information

Used simplifier rules: abs-06: ⊦ 0 < abs(i) ↔ i ≠ 0; from specification int-abs%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%lep-02: ⊦ i + j ≤ i + j0 ↔ j ≤ j0; from specification int-abs%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%eq: ⊦ i = i + j ↔ j = 0; from specification int-basic2