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Proof step 9 from proof estimate-01 (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 10:
j1 < j, j < i, j0 < i0, 0 < i, 0 < j, 1 < i, 0 < i0, i1 < i0, j * i0 < i1 * j + j1, i * i0 ≤ i1 * j + j1, i1 ≤ j0, 0 ≤ j1 ⊦

Rule argument

fma: j * i0 < i1 * j + j1

Additional information

Used simplifier rules: ⊦ i < j ↔ ¬ j ≤ i; (ss)%forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs% ⊦ 0 < i → (i * j ≤ i * i0 ↔ j ≤ i0); (s)% ⊦ i < j → (j ≤ i ↔ false); (as)%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