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Proof step 5 from proof estimate-01 (previous step)

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

User applied rule cut formula

And obtained the following new goals

Rule argument

fma: i1 * j + j1 < i * i0

Additional information

Used simplifier rules: ls-forward: ⊦ i * j < i * j0 → i ≠ 0; (forward) from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%lf-02: ⊦ i < j ∧ j = i0 → i < i0; (forward) from specification int-basic1%ls-pos: ⊦ 0 < i → (i * j < i * j0 ↔ j < j0); from specification int-mult%irref: ⊦ ¬ i < i; from specification int-basic1 Used formulas: i1 * j + j1 < i * i0