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Proof step 7 from proof longshiftzero-carry-01 (previous step)

0 ≤ i + band(4294967295, j) + band(4294967295, j0), i ≤ 1, 0 ≤ i, i < (i + band(4294967295, j) + band(4294967295, j0)) >> 32, 1 < (i + band(4294967295, j) + band(4294967295, j0)) >> 32, 0 < (i + band(4294967295, j) + band(4294967295, j0)) >> 32 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ 0 ≤ i ∧ 0 ≤ j → i >> j = i / 2 ^ j
Proof step 9:
0 ≤ i + band(4294967295, j) + band(4294967295, j0) ∧ 0 ≤ 32, 0 ≤ i + band(4294967295, j) + band(4294967295, j0), i ≤ 1, 0 ≤ i, i < (i + band(4294967295, j) + band(4294967295, j0)) / 2 ^ 32, 1 < (i + band(4294967295, j) + band(4294967295, j0)) / 2 ^ 32, 0 < (i + band(4294967295, j) + band(4294967295, j0)) / 2 ^ 32 ⊦

Rule argument

name: shiftright-pos-div rotate: F subst: [j, i] → [32, i + band(4294967295, j) + band(4294967295, j0)]

Additional information

Used simplifier rules: ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false); Used terms: 32, i + band(4294967295, j) + band(4294967295, j0)