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Proof step 9 from proof zero-not (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: rew-eqzero seq: ⊦ i + j = 0 ↔ i = ~ j subst: [j, i] → [i0, i] flags: <all paths>

Additional information

Used simplifier rules: Minus-def: ⊦ ~ i = 0 - i;%sub-ls: ⊦ i - j < i0 ↔ i < j + i0;%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j;% ⊦ 0 + i = i; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ i < j → ¬ j < i; (s) Used terms: i0, i