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Proof step 5 from proof ls-add (previous step)

i0 * j + j1 < j, j1 < j, 0 < j, 0 ≤ j1 ⊦ i0 ≤ 0

User applied rule apply lemma

And obtained the following new goals

Proof step 6:
j * i + j0 < j * i0, abs(j0) < j ⊦ i ≤ i0
Proof step 7:
0 < j, j1 < j, i0 * j + j1 < j, 0 ≤ j1, i0 ≤ 1 ⊦ i0 ≤ 0

Rule argument

spec: <toplevel> name: modlsp-02 seq: j * i + j0 < j * i0, abs(j0) < j ⊦ i ≤ i0 subst: [j, i, j0, i0] → [j, i0, j1, 1]

Additional information

Used simplifier rules: one: ⊦ 1 * i = i;%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;% ⊦ 0 ≤ i → abs(i) = i; (s) Used terms: j, i0, j1, 1