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Proof step 2 from proof prime-divides-pot (previous step)

i * j = i0 ^ j0, prime(i), 0 ≤ j0 ⊦ i | i0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ 0 < i → j ^ i = j ^ i -1 * j
Proof step 4:
0 < j0, i * j = i0 ^ j0 -1 * i0, prime(i), 0 ≤ j0 ⊦ i | i0

Rule argument

spec: int-pot inst: name: Pot-pos seq: ⊦ 0 < i → j ^ i = j ^ i -1 * j subst: [i, j] → [j0, i0] flags: rewrite

Additional information

Used simplifier rules: lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%anti: ⊦ i ≤ j → (j ≤ i ↔ i = j); from specification int-abs%Pot-zero: ⊦ j ^ 0 = 1; from specification int-pot%eq-one: ⊦ i * j = 1 ↔ abs(i) = 1 ∧ i = j; from specification int-mult%prime-abs: ⊦ prime(j) → abs(j) = j; from specification int-gcd%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%prime-one: ⊦ i ≤ 1 → ¬ prime(i); from specification int-gcd Used terms: j0, i0