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Proof step 7 from proof ple-01 (previous step)

0 < j, i0 < j0 ⊦ j0 = i0, i0 < j + j0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-basic2 name: ex-ls-add seq: ⊦ i < j ↔ (∃ i0. j = i + i0 ∧ 0 < i0) subst: [j, i] → [j0, i0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ i = i + j ↔ j = 0; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ i < i + j ↔ 0 < j; (s)% ⊦ 0 < i ∧ 0 < j → 0 < i + j; (s) Used terms: j0, i0