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Proof step 3 from proof mod-pred-02 (previous step)

i = i0 + 1, 0 < i, 0 < j ⊦ i % j = 0, i % j = i0 % j + 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
0 < j, 0 ≤ i0 ⊦ (i0 + 1) % j = 0, (i0 + 1) % j = i0 % j + 1

Rule argument

Additional information

Used simplifier rules: forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) 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%mone-06: ⊦ ~1 < i ↔ 0 ≤ i; from specification int-abs%numls-02: ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0; from specification int-abs