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Proof step 9 from proof nummult-le-01 (previous step)

j + 1 = i * (i1 + 1) + j0, j0 ≤ 0, abs(j0) < i, j < i, j < 0, 0 < i, j0 < i, j + 1 < i ⊦ i * i0 ≤ j ↔ i0 ≤ i1, i = j + 1

User applied rule cut formula

And obtained the following new goals

Proof step 10:
j = i * (i1 + 1) + j0 - 1, j + 1 = i * (i1 + 1) + j0, j0 ≤ 0, abs(j0) < i, j < i, j < 0, 0 < i, j0 < i, j + 1 < i ⊦ i * i0 ≤ j ↔ i0 ≤ i1, i = j + 1

Rule argument

fma: j = i * (i1 + 1) + j0 - 1

Additional information

Used simplifier rules: sub-eq: ⊦ i - j = i0 ↔ i = i0 + j; from specification int-abs Used formulas: j = i * (i1 + 1) + j0 - 1