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Proof step 35 from proof intshiftrsign-2pot-neg-01 (previous step)

j < 32, i0 < j, 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 - 2 ^ (j - 1))) / (2 * 2 ^ (j - 1))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 36:
j ≠ 0 ⊦ (2 * i) / (2 * j) = i / j
Proof step 37:
¬ 2 ^ (j - 1) ≠ 0, j < 32, i0 < j, 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 - 2 ^ (j - 1))) / (2 * 2 ^ (j - 1))

Rule argument

seq: j ≠ 0 ⊦ (2 * i) / (2 * j) = i / j subst: [j, i] → [2 ^ (j - 1), i0 + 1 - 2 ^ (j - 1)] rotate: F spec: int-div inst: name: div-two-01

Additional information

Used simplifier rules: ⊦ i + j = j + i; Used terms: 2 ^ (j - 1), i0 + 1 - 2 ^ (j - 1)