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Proof step 23 from proof longshiftzero-carry-01 (previous step)

i + band(4294967295, j) < i + 4294967296, 0 < i + band(4294967295, j), band(4294967295, j0) < 4294967296, 4294967296 < i + band(4294967295, j), 8589934592 ≤ i + band(4294967295, j) + band(4294967295, j0), 0 < i + band(4294967295, j) + band(4294967295, j0), i ≤ 1, 0 ≤ i, 0 ≤ i + band(4294967295, j) + band(4294967295, j0), i ≤ (i + band(4294967295, j) + band(4294967295, j0) - 4294967296) / 4294967296, 0 < (i + band(4294967295, j) + band(4294967295, j0) - 4294967296) / 4294967296 ⊦

User applied rule cut formula

And closed the goal!

Rule argument

fma: 4294967296 < i + 4294967296

Additional information

Used simplifier rules: band-commutativity: ⊦ band(i, j) = band(j, i);%band-commutativity: ⊦ band(i, j) = band(j, i);%band-max-02: ⊦ 0 ≤ i ∧ i ≤ i0 → ¬ i0 < band(i, j);%band-associativity: ⊦ band(i, band(i0, j)) = band(band(i, i0), j);% ⊦ i + 0 = i;% ⊦ i ≤ j → (j ≤ i ↔ i = j);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i + j < i + i0 ↔ j < i0;% ⊦ 0 < i → (i ≤ 1 ↔ i = 1);% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ ~1 < i ↔ 0 ≤ i;% ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0;%i + 1 = i0 ⊦ j < (* i0) → ¬ (* i) < j; Used formulas: 4294967296 < i + 4294967296