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Proof step 14 from proof count-rec (previous step)

i + 1 ≤ i2 + 1, i1 + i = i2 + 1, 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, i2) + (i2 + 1)' = i ' + (count-i2j(i + 1, i2 + 1 - 1) + (i2 + 1))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: le-add: ⊦ i + j ≤ i0 + j ↔ i ≤ i0; from specification int-abs%app-03: ⊦ ints + ints0 = ints1 + ints0 ↔ ints = ints1; from specification list[intlista]%a: ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1; from specification list[intlista]%Last: ⊦ ints + i = ints + i '; from specification list[intlista]%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%ax-04: ⊦ i + 0 = i; from specification int-basic2%numsub: ⊦ (* i) + i0 - (* j) = (i - j) + i0; from specification int-abs