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Proof step 8 from proof div-ls (previous step)

j2 < j, j1 ≤ j0, i0 * j + j2 < j1 * j, j0 ≤ i0, 0 < j1, 0 < j0, 0 < j, 0 ≤ j2, 0 ≤ i0, j1 ≤ i0, 0 < i0 ⊦ j = 0

User applied rule cut formula

And obtained the following new goals

Rule argument

fma: i0 = j1

Additional information

Used simplifier rules: anti: ⊦ i ≤ j → (j ≤ i ↔ i = j); from specification int-abs%mods-ls-04: ⊦ j0 < j ∧ 0 ≤ i ∧ 0 ≤ i0 ∧ 0 ≤ j0 → (i * j + j0 < i0 * j ↔ i < i0); from specification int-mult%lenls: ⊦ i ≤ j → ¬ j < i; from specification int-abs%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used formulas: i0 = j1