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Proof step 13 from proof longshiftzero-carry-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
0 < j, j ≤ i ⊦ i / j = (i - j) / j + 1
Proof step 15:
0 < 4294967296 ∧ 4294967296 ≤ 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 + 1, 1 < (i + band(4294967295, j) + band(4294967295, j0) - 4294967296) / 4294967296 + 1, 0 < (i + band(4294967295, j) + band(4294967295, j0) - 4294967296) / 4294967296 + 1, 4294967296 ≤ i + band(4294967295, j) + band(4294967295, j0), 0 < i + band(4294967295, j) + band(4294967295, j0) ⊦

Rule argument

seq: 0 < j, j ≤ i ⊦ i / j = (i - j) / j + 1 subst: [j, i] → [4294967296, i + band(4294967295, j) + band(4294967295, j0)] rotate: F spec: int-div inst: name: div-rec

Additional information

Used simplifier rules: i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j; Used terms: 4294967296, i + band(4294967295, j) + band(4294967295, j0)