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Proof step 3 from proof intshiftrsign-2pot-neg-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ i < 0 ∧ 0 < j ∧ j < 32 → i i>> j = (i - 1) / 2 i>> (j - 1)
Proof step 5:
i < 0 ∧ 0 < j ∧ j < 32, j < 32, i < 0, 0 < j, ∀ i, j0. i→n(j0) < i→n(j) → true → i < 0 ∧ 0 < j0 ∧ j0 < 32 → i i>> j0 = (i - (2 ^ j0 - 1)) / 2 ^ j0 ⊦ (i - 1) / 2 i>> (j - 1) = (i + 1 - 2 ^ j) / 2 ^ j

Rule argument

name: intshiftrsign-rec-neg rotate: F subst: [j, i] → [j, i]

Additional information

Used simplifier rules: ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);%j0 ≠ 0, j ≤ j0 ⊦ i < (* j) → i < (* j0); Used terms: j, i