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Proof step 4 from proof short-mult-max (previous step)

0 < i, 0 < j, i < 256, i * j < 256 * j, 0 ≤ j, j ≤ 256, 65536 ≤ i * j ⊦ i = 0

User applied rule cut formula

And obtained the following new goals

Proof step 5:
i * j < 256 * j, i < 256, 0 < j, 0 < i, 65536 < 256 * j, 65536 ≤ i * j, j ≤ 256, 0 ≤ j ⊦ i = 0

Rule argument

fma: 65536 < 256 * j

Additional information

Used simplifier rules: ls-pos: ⊦ 0 < i → (i * j < i * j0 ↔ j < j0);%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%le-pos: ⊦ 0 < i → (i * j ≤ i * i0 ↔ j ≤ i0);%j0 ≠ 0, j ≤ j0 ⊦ i < (* j) → i < (* j0); (s)% ⊦ i < j ↔ ¬ j ≤ i; (ss)%forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs% ⊦ i < j → (j ≤ i ↔ false); (as) Used formulas: 65536 < 256 * j