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Proof step 8 from proof div2-2pot-neg (previous step)

2 ≠ 0, ~ abs(i) < j, ~ abs(i) < 0, 0 < j, ~ abs(i) + 1 < j ⊦ ~((abs(i) * 2 ^ j) / 2) = ~ abs(i) * 2 ^ (j - 1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ 0 ≤ i ∧ 0 < j → (i * 2 ^ j) / 2 = i * 2 ^ (j - 1)

Rule argument

spec: int-pot inst: name: div2-2pot-02 seq: ⊦ 0 ≤ i ∧ 0 < j → (i * 2 ^ j) / 2 = i * 2 ^ (j - 1) subst: [j, i] → [j, abs(i)] flags: rewrite, current

Additional information

Used simplifier rules: minus-left: ⊦ ~ i * j = ~(i * j); from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%neg-12: ⊦ ~ i = ~ j ↔ i = j; from specification int-abs%neg-13: ⊦ ~ i < j ↔ 0 < j + i; from specification int-abs%neg-05: ⊦ ~ i < 0 ↔ 0 < i; from specification int-abs%abs-06: ⊦ 0 < abs(i) ↔ i ≠ 0; from specification int-abs%neg-15: ⊦ i + ~ j = i - 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%sub-ls: ⊦ i - j < i0 ↔ i < j + i0; from specification int-abs%abs-03: ⊦ 0 ≤ abs(i); from specification int-abs Used terms: j, abs(i)