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Proof step 12 from proof div-ls-mone (previous step)

0 < j + j0, j0 < 0, i0 < j + j0, i0 * j + j0 < 0, j0 < j, i0 < j, 0 < j, i0 < 0, i0 ≤ 0 ⊦ i0 < ~1 ↔ j * (2 + i0) + j0 ≤ 0

User applied rule cut formula

And obtained the following new goals

Proof step 13:
i0 < 0, 0 < j, i0 < j, j0 < j, i0 * j + j0 < 0, i0 < j + j0, j0 < 0, 0 < j + j0, i0 ≤ 0 ⊦ i0 < ~1 ↔ j * (2 + i0) + j0 ≤ 0, i0 = ~1

Rule argument

fma: i0 = ~1

Additional information

Used simplifier rules: add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ 1 * i = i; (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult% ⊦ i < j → (j ≤ i ↔ false); (as) Used formulas: i0 = ~1