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Proof step 26 from proof shiftright-shift (previous step)

0 ≤ j + j0, 0 ≤ i, 0 ≤ j0, 0 ≤ j, j + j0 < 32 ⊦ (i >> j) >> j0 = i / (2 ^ j * 2 ^ j0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 27:
⊦ 0 ≤ i ∧ 0 ≤ j → i >> j = i / 2 ^ j
Proof step 28:
0 ≤ i >> j ∧ 0 ≤ j0, 0 ≤ j + j0, 0 ≤ i, 0 ≤ j0, 0 ≤ j, j + j0 < 32 ⊦ (i >> j) / 2 ^ j0 = i / (2 ^ j * 2 ^ j0)

Rule argument

name: shiftright-pos-div rotate: F subst: [j, i] → [j0, i >> j]

Additional information

Used simplifier rules: shiftright-not-neg: ⊦ 0 ≤ i → ¬ i >> j < 0;% ⊦ i + j = j + i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false); Used terms: j0, i >> j