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Proof step 5 from proof longshiftzero-carry-01 (previous step)

i ≤ 1, 0 ≤ i, i < >>>(64, i + band(4294967295, j) + band(4294967295, j0), 32), 1 < >>>(64, i + band(4294967295, j) + band(4294967295, j0), 32), 0 < >>>(64, i + band(4294967295, j) + band(4294967295, j0), 32) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ 0 ≤ i → >>>(n, i, j) = i >> j
Proof step 7:
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 ⊦

Rule argument

name: shiftzero-pos rotate: F subst: [j, i, n] → [32, i + band(4294967295, j) + band(4294967295, j0), 64]

Additional information

Used simplifier rules: band-32-not-neg: ⊦ ¬ band(4294967295, i) + band(4294967295, j) < 0;%band-associativity: ⊦ band(i, band(i0, j)) = band(band(i, i0), j);%band-commutativity: ⊦ band(i, j) = band(j, i);% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ i + j < j ↔ i < 0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used terms: 32, i + band(4294967295, j) + band(4294967295, j0), 64