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Proof step 8 from proof mod-nls (previous step)

j < 0, 0 < i1 * j + i0, 0 ≤ i0, 0 ≤ i1, i0 ≤ i1 ⊦ i1 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: zero-gr-add-02 seq: ⊦ 0 ≤ i0 ∧ i0 ≤ i1 ∧ j < 0 → ¬ 0 < i1 * j + i0 subst: [i0, j, i1] → [i0, j, i1] flags: <all paths>

Additional information

Used simplifier rules: zero-gr-add-02: ⊦ 0 ≤ i0 ∧ i0 ≤ i1 ∧ j < 0 → ¬ 0 < i1 * j + i0;%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;% ⊦ i ≠ j → (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 Used terms: i0, j, i1