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Proof step 6 from proof auxexdivmod-01 (previous step)

0 < j, 0 ≤ i, i * j ≤ i ⊦ 0 < i, ∃ i0. i0 * j ≤ i ∧ i < i0 * j + j ∧ 0 ≤ i0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
0 < j ⊦ ∃ i0. i0 * j ≤ 0 ∧ 0 < i0 * j + j ∧ 0 ≤ i0

Rule argument

Additional information

Used simplifier rules: Mult-zero: ⊦ i * 0 = 0;%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;% ⊦ i ≤ j → (j ≤ i ↔ i = j); (s)% ⊦ i < j ↔ ¬ j ≤ i; (ss)