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Proof step 13 from proof intshiftrsign-2pot-neg-01 (previous step)

0 < j, j < 32, 0 ≤ j, i0 < 0, ∀ i, j0. i→n(j0) < i→n(j) → true → i < 0 ∧ 0 < j0 ∧ j0 < 32 → i i>> j0 = (i - (2 ^ j0 - 1)) / 2 ^ j0 ⊦ j = 1, (i0 + 1 - 2 ^ (j - 1)) / 2 ^ (j - 1) = (2 * (i0 + 1) - 1 + 2 ^ j) / 2 ^ j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ 0 < i → j ^ i = j ^ i -1 * j
Proof step 15:
0 < j, 0 < j, j < 32, 0 ≤ j, i0 < 0, ∀ i, j0. i→n(j0) < i→n(j) → true → i < 0 ∧ 0 < j0 ∧ j0 < 32 → i i>> j0 = (i - (2 ^ j0 - 1)) / 2 ^ j0 ⊦ j = 1, (i0 + 1 - 2 ^ (j - 1)) / 2 ^ (j - 1) = (2 * (i0 + 1) - 1 + 2 ^ j -1 * 2) / (2 ^ j -1 * 2)

Rule argument

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

Additional information

Used terms: j, 2