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

j2 < j0, j1 < j0, 0 < i0, 0 < j0, i1 < i2, j1 < i0, 0 < i2, 0 ≤ i1, i0 ≤ j0, i2 * j0 + j2 ≤ i1 * i0 + j1, 0 ≤ j1, 0 ≤ j2, 0 ≤ i2 ⊦ i0 = 0, j0 = 0

User applied rule cut formula

And obtained the following new goals

Rule argument

fma: i2 * j0 + j2 ≤ i1 * j0 + j1

Additional information

Used simplifier rules: ⊦ i ≤ j ↔ ¬ j < i; (ss)%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs% ⊦ i + j < i + i0 ↔ j < i0; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%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% ⊦ i ≠ j → (i ≤ j ↔ i < j); (s)% ⊦ 0 < i → (i * j < i * j0 ↔ j < j0); (s)% ⊦ i ≤ j → ¬ j < i; (s) Used formulas: i2 * j0 + j2 ≤ i1 * j0 + j1