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Proof step 4 from proof mod-nls (previous step)

j < i, j < 0, i0 < i, 0 < (i - 1) * j + i0, 0 < i, 0 ≤ i0, j + 1 < i ⊦

Heuristic elimination applied rule insert elim lemma

And closed the goal!

Rule argument

spec: int-abs inst: name: elim-sub seq: ⊦ i0 = i - j ↔ i = i0 + j subst: [i, j, i0] → [i, 1, i1] flags:

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;%succ-02: ⊦ i < j + 1 ↔ 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% ⊦ i0 = i - j ↔ i = i0 + j; (elim) Used terms: i, 1, i1