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Proof step 29 from proof shiftright-shift (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 30:
⊦ 0 ≤ i ∧ 0 ≤ j → i >> j = i / 2 ^ j
Proof step 31:
0 ≤ i ∧ 0 ≤ j, 0 ≤ j + j0, 0 ≤ i, 0 ≤ j0, 0 ≤ j, j + j0 < 32, 0 ≤ i / 2 ^ j ⊦ (i / 2 ^ j) / 2 ^ j0 = i / (2 ^ j * 2 ^ j0)

Rule argument

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

Additional information

Used simplifier rules: ⊦ i + j = j + i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false); Used terms: j, i