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Proof step 9 from proof prime-divides-pot-01 (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 10:
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) ⊦ i1 = 0, i | i0

Rule argument

fma: i1 = 0

Additional information

Used simplifier rules: Pot-zero: ⊦ j ^ 0 = 1; from specification int-pot%prime-divides-one: ⊦ prime(i) → ¬ i | 1; from specification int-gcd Used formulas: i1 = 0