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Proof step 21 from proof div-ls-mone (previous step)

0 < j * (2 + i0) + j0, i0 < 0, 0 < j + j0, j0 < 0, i0 < j + j0, j0 < j, i0 < j, 0 < j, i0 < ~1, ~2 ≤ i0 ⊦ i0 = ~1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-basic1 name: ls-rec seq: ⊦ i ≠ j -1 → (i < j ↔ i < j -1) subst: [j, i] → [~1, i0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ i ≠ j → (i ≤ j ↔ i < j); (s)% ⊦ i < 0 → (~2 < i ↔ i = ~1); (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ i * 0 = 0; (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult% ⊦ i + 0 = i; (s)% ⊦ i < j → ¬ j < i; (s) Used terms: ~1, i0