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Proof step 8 from proof prime-divides-pot-01 (previous step)

j = i1 + 1, 0 < j, prime(i), i | i0 ^ i1, ∀ j0, i, i0. i→n(j0) < i→n(j) → prime(i) ∧ 0 < j0 → (i | i0 ^ j0 ↔ i | i0) ⊦ i | i0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
prime(i), i | i0 ^ i1, 0 ≤ i1, ∀ j0, i, i0. i→n(j0) < i→n(i1 + 1) → prime(i) ∧ 0 < j0 → (i | i0 ^ j0 ↔ i | i0) ⊦ i | i0

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