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Proof step 16 from proof nummult-ls-03 (previous step)

j + 1 = i2 * (i3 + 1) + j0, i3 * i2 + j0 < 0, 0 < i2, j0 < i2, j < 0, abs(j0) < i2, j0 ≤ 0, i3 * i2 + j0 ≤ j ⊦ j < i2 * i0 ↔ ¬ i0 ≤ i3

User applied rule cut formula

And obtained the following new goals

Proof step 17:
j + 1 = i2 * (i3 + 1) + j0, j = i2 * (i3 + 1) + j0 - 1, abs(j0) < i2, j < 0, j0 < i2, 0 < i2, i3 * i2 + j0 < 0, i3 * i2 + j0 ≤ j, j0 ≤ 0 ⊦ j < i2 * i0 ↔ ¬ i0 ≤ i3

Rule argument

fma: j = i2 * (i3 + 1) + j0 - 1

Additional information

Used simplifier rules: ⊦ i - j = i0 ↔ i = i0 + j; (s) Used formulas: j = i2 * (i3 + 1) + j0 - 1