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Proof step 7 from proof count-rec (previous step)

i ≤ i1 + i, 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 simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
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)

Rule argument

Additional information

Used simplifier rules: add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%lep: ⊦ i ≤ i + j ↔ 0 ≤ j; from specification int-abs%Last: ⊦ ints + i = ints + i '; from specification list[intlista]