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Proof step 2 from proof bint-carry (previous step)

i0 ≤ 1, 0 ≤ i0 ⊦ ((i0 + band(4294967295, i) + band(4294967295, j)) l>>> 32)∈bint

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

name: inbint rotate: F subst: [i] → [ ( i0 + band(4294967295, i) + band(4294967295, j)) l>>> 32]

Additional information

Used simplifier rules: ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < (* j) ∧ j < 0 → i < 0; (forward)%⊦ 0 ≤ i ∧ i ≤ 1 → ¬ (i + band(4294967295, j) + band(4294967295, j0)) l>>> 32 < 0;% ⊦ band(i, band(i0, j)) = band(band(i, i0), j);% ⊦ band(i, j) = band(j, i);% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward)%⊦ 0 ≤ i ∧ i ≤ 1 → ¬ 1 < (i + band(4294967295, j) + band(4294967295, j0)) l>>> 32; Used terms: (i0 + band(4294967295, i) + band(4294967295, j)) l>>> 32