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Proof step 5 from proof product-pot-rec (previous step)

i = i0, ∀ i. i ∈ ints0 → Π ints0 = i ^ n→i(#oc(i, ints0)) * Π(ints0 -l i) ⊦ i0 * Π ints0 = i ^ (n→i(#oc(i, i0 ')) + n→i(#oc(i, ints0))) * Π((i0 ' + ints0) -l i), i ≠ i0 ∧ ¬ i ∈ ints0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
∀ i. i ∈ ints0 → Π ints0 = i ^ n→i(#oc(i, ints0)) * Π(ints0 -l i) ⊦ i0 * Π ints0 = i0 ^ (1 + n→i(#oc(i0, ints0))) * Π(ints0 -l i0)

Rule argument

Additional information

Used simplifier rules: a: ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1; from specification list[intlista]%del-y: ⊦ (i ' + ints) -l i = ints -l i; from specification list-del[intlista]%one: ⊦ #oc(i, i ') = 1; from specification list-perm[intlista]