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Proof step 2 from proof le-add-02 (previous step)

i0 < i ⊦ i0 < i + j0, j0 < 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
i + j < i0 + j0, ¬ j < j0 ⊦ i < i0

Rule argument

spec: int-basic2 inst: name: pls-04 seq: i + j < i0 + j0, ¬ j < j0 ⊦ i < i0 subst: [i, j, i0, j0] → [i0, j0, i + j0, 0] flags: rewrite

Additional information

Used simplifier rules: add-zero-rev: ⊦ 0 + i = i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%ls-add-both: ⊦ i < j → i1 + i < i1 + j; from specification int-basic2 Used terms: i0, j0, i + j0, 0