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Proof step 2 from proof pot2-suble (previous step)

0 < i ⊦ j + 2 ^ (i - 1) ≤ 2 ^ i ↔ j ≤ 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

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: sub-pred: ⊦ i -1 = i - 1; from specification int-abs%numle-08: ⊦ i + j ≤ (* i1) * i ↔ j ≤ (i1 - 1) * i; from specification int-mult%one: ⊦ 1 * i = i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: i, 2