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Proof step 8 from proof divides-pot-prime (previous step)

j0 = i0 + 1, prime(i), 0 < j0, i | j ^ i0, ∀ j1, i, j. i→n(j1) < i→n(j0) → prime(i) ∧ 0 < j1 → (i | j ^ j1 ↔ i | j) ∨ j = 0 ⊦ j = 0, i | j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
i | j ^ i0, prime(i), 0 ≤ i0, ∀ j1, i, j. i→n(j1) < i→n(i0 + 1) → prime(i) ∧ 0 < j1 → (i | j ^ j1 ↔ i | j) ∨ j = 0 ⊦ j = 0, i | j

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