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Proof step 4 from proof intshiftrsign-2pot-pos (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ 0 ≤ i ∧ 0 < j ∧ j < 32 → i i>> j = i / 2 i>> (j - 1)
Proof step 6:
0 ≤ i ∧ 0 < j ∧ j < 32, 0 < j, 0 ≤ i, j < 32, ∀ i, j0. i→n(j0) < i→n(j) → j0 < 32 ∧ 0 ≤ i ∧ 0 < j0 → i i>> j0 = i / 2 ^ j0 ⊦ i / 2 i>> (j - 1) = i / 2 ^ j

Rule argument

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

Additional information

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