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

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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

Rule argument

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;%zero-gr: ⊦ 0 < i → (0 < i * j ↔ 0 < j);%numlslsdel-01: i0 ≠ 0, i0 < i ⊦ (* i) < j → (* i0) < j; from specification int-basic1%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1%numlelsdel: j0 ≠ 0, j ≤ j0 ⊦ i < (* j) → i < (* j0); from specification int-abs