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Proof step 9 from proof countFun-last (previous step)

¬ i3 + i < i, ~1 ≤ i3, ∀ i1, i2, intfun. i→n(i1 - i2) < i→n(i3) → i2 ≤ i1 + 1 → countFun(i2, i1 + 1, intfun) = countFun(i2, i1, intfun) + intfun(i1 + 1) ' ⊦ countFun(i, (i3 + i) + 1, intfun) = countFun(i, i3 + i, intfun) + intfun((i3 + i) + 1) '

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%numleledel-01: i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j; from specification int-abs%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%ls: ⊦ i + j < j ↔ i < 0; from specification int-basic2