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Proof step 9 from proof bint-carry-01 (previous step)

0 < (band(4294967295, i) + band(4294967295, j)) l>>> 32, 2147483647 < (band(4294967295, i) + band(4294967295, j)) l>>> 32 ⊦

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

seq: ⊦ 0 ≤ i ∧ i ≤ 1 → ¬ 1 < ( i + band(4294967295, j) + band(4294967295, j0)) l>>> 32 subst: [i, j, j0] → [0, i, j] rotate: F spec: intops inst: name: longshiftzero-carry-01

Additional information

Used simplifier rules: ⊦ i + 0 = i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ band(i, j) = band(j, i);%i0 ≠ 0, i0 < i ⊦ (* i) < j → (* i0) < j; Used terms: 0, i, j