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Proof step 6 from proof zero-not (previous step)

i + i0 = 0, 0 < j, i0 < j, i0 + 1 < i, 1 < j, 0 < i, i0 < 0, i < j, i0 < i, 2 + i0 < j ⊦ i < i0 + j, 0 < i0 + j

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-abs inst: name: rew-eqzero seq: ⊦ i + j = 0 ↔ i = ~ j subst: [j, i] → [i0, i] flags: rewrite, current

Additional information

Used simplifier rules: Minus-def: ⊦ ~ i = 0 - i;%sub-ls-01: ⊦ i < j - i0 ↔ i + i0 < j;%numls-03: ⊦ i + (* j) < (* j0) ↔ i < j0 - j;%zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j;%sub-ls: ⊦ i - j < i0 ↔ i < j + i0;%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j;%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%add-zero-rev: ⊦ 0 + i = i; from specification int-basic2%zero-01: ⊦ i < 0 ∧ j < 0 → i + j < 0; from specification int-basic2%lf-01: ⊦ i < j ∧ j < i0 → i +1 < i0; (forward) from specification int-basic1%trans: ⊦ i < j ∧ j < j0 → i < j0; (forward) from specification int-basic1%numlsf: ⊦ i < (* j) ∧ j < 0 → i < 0; (forward) from specification int-basic1 Used terms: i0, i