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Proof step 27 from proof intshiftrsign-2pot-neg (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 28:
j ≠ 0 ⊦ (i * j) / j = i
Proof step 29:
¬ 2 ^ (j - 1) ≠ 0, j0 * 2 ^ (j - 1) i>> (j - 1) = (j0 * 2 ^ (j - 1)) / 2 ^ (j - 1), 0 < j, j < 32, j0 * 2 ^ j < 0, ∀ i, j0. i→n(j0) < i→n(j) → true → i < 0 ∧ i % 2 ^ j0 = 0 ∧ 0 < j0 ∧ j0 < 32 → i i>> j0 = i / 2 ^ j0 ⊦ (j0 * 2 ^ (j - 1)) / 2 ^ (j - 1) = j0

Rule argument

seq: j ≠ 0 ⊦ (i * j) / j = i subst: [j, i] → [2 ^ (j - 1), j0] rotate: F spec: int-div inst: name: div-mult-03

Additional information

Used terms: 2 ^ (j - 1), j0