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Proof step 3 from proof modlsp-04 (previous step)

j * i < j * i0 + j0, j < 0, abs(j0) + j < 0, i < i0 ⊦

User applied rule apply lemma

And obtained the following new goals

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, ~ j0, i]

Additional information

Used simplifier rules: minus-left: ⊦ ~ i * j = ~(i * j);%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;% ⊦ i < j → (j ≤ i ↔ false); (as)% ⊦ ~ i + ~ j = ~(i + j); (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ ~ j < ~ i ↔ i < j; (s)% ⊦ abs(~ i) = abs(i); (s)% ⊦ i < ~ j ↔ i + j < 0; (s) Used terms: ~ j, i0, ~ j0, i