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Proof step 2 from proof modlsp-04 (previous step)

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

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: modlsp-02 seq: j * i + j0 < j * i0, abs(j0) < j ⊦ i ≤ i0 subst: [j, i, j0, i0] → [~ j, i0, ~ j0, i] flags: current, []

Additional information

Used simplifier rules: minus-left: ⊦ ~ i * j = ~(i * j);%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs%neg-11: ⊦ ~ i + ~ j = ~(i + j); from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%neg-01: ⊦ ~ j < ~ i ↔ i < j; from specification int-abs%abs-neg: ⊦ abs(~ i) = abs(i); from specification int-abs%neg-07: ⊦ i < ~ j ↔ i + j < 0; from specification int-abs%zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs Used terms: ~ j, i0, ~ j0, i