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Proof step 8 from proof estimate-01 (previous step)

0 ≤ j1, i1 < i0, j1 < j, 1 < i, 0 < i, 0 < j, 0 < i0, i1 ≤ j0, j0 < i0, j < i, i * i0 ≤ i1 * j + j1 ⊦

User applied rule cut formula

And obtained the following new goals

Rule argument

fma: j * i0 < i1 * j + j1

Additional information

Used simplifier rules: lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs%le-pos: ⊦ 0 < i → (i * j ≤ i * i0 ↔ j ≤ i0); from specification int-mult%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used formulas: j * i0 < i1 * j + j1