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Proof step 1 from proof fac-add (conclusion)

⊦ 0 ≤ i ∧ 0 ≤ j → fac(i + j) = fac(i) * Π countFun(1, j, λ j0. i + j0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
0 ≤ i, 0 ≤ j ⊦ fac(i + j) = fac(i) * Π countFun(1, j, λ j0. i + j0)

Rule argument

Additional information

Used simplifier rules: forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs