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Proof step 2 from proof eq2 (previous step)

2 ^ i = 2 ⊦ i = 1

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 < i, 2 ^ i = 2 ⊦ i = 1

Rule argument

spec: int-pot inst: name: Pot-pos seq: ⊦ 0 < i → j ^ i = j ^ i -1 * j subst: [i, j] → [i, 2] flags: rewrite, current

Additional information

Used simplifier rules: eq-one: ⊦ 2 ^ i = 1 ↔ i = 0;%sub-pred: ⊦ i -1 = i - 1; from specification int-abs%eq-same-02: ⊦ 0 < i → (i * j = i ↔ j = 1); from specification int-mult%sub-eq: ⊦ i - j = i0 ↔ i = i0 + j; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: i, 2