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Proof step 8 from proof count-rec (previous step)

0 ≤ i1, ∀ j0, i0. i→n(j0 - i0) < i→n(i1) → i0 ≤ j0 → count-i2j(i0, j0) = i0 ' + count-i2j(i0 + 1, j0) ⊦ count-i2j(i, i1 + i - 1) + (i1 + i)' = i ' + count-i2j(i + 1, i1 + i)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Rule argument

spec: int-abs inst: name: elim-sub seq: ⊦ i0 = i - j ↔ i = i0 + j subst: [i, j, i0] → [i1 + i, 1, i2] flags:

Additional information

Used simplifier rules: ⊦ i0 = i - j ↔ i = i0 + j; (elim) Used terms: i1 + i, 1, i2