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Proof step 5 from proof div2-2pot-02 (previous step)

0 ≤ i, 0 ≤ i0 ⊦ (i * 2 ^ (i0 + 1)) / 2 = i * 2 ^ i0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ 0 < i → j ^ i = j ^ i -1 * j

Rule argument

spec: <toplevel> name: Pot-pos seq: ⊦ 0 < i → j ^ i = j ^ i -1 * j subst: [i, j] → [i0 + 1, 2] flags: <all paths>

Additional information

Used simplifier rules: ⊦ (i + 1)-1 = i; (s)%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%j ≠ 0 ⊦ (i * j) / j = i; (s)%commutativity: ⊦ i * j = j * i; from specification int-mult% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0; (s)% ⊦ ~1 < i ↔ 0 ≤ i; (s)% ⊦ i ≤ j ↔ ¬ j < i; (ss)% ⊦ i ≤ j → (j < i ↔ false); (as) Used terms: i0 + 1, 2