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Proof step 6 from proof fac-add (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: intlist inst: name: countFun-base seq: ⊦ j < i → countFun(i, j, intfun) = [] subst: [intfun, j, i] → [λ j0. i + j0, 0, 1] flags: rewrite

Additional information

Used simplifier rules: prod-empty: ⊦ Π [] = 1; from specification intlist Used terms: λ j0. i + j0, 0, 1