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Proof step 8 from proof product-pot-rec (previous step)

0 < n→i(#oc(i0, ints0)) + 1, ∀ i. i ∈ ints0 → Π ints0 = i ^ n→i(#oc(i, ints0)) * Π(ints0 -l i) ⊦ i0 * Π ints0 = (i0 ^ (n→i(#oc(i0, ints0)) + 1)-1 * i0) * Π(ints0 -l i0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
∀ i. i ∈ ints0 → Π ints0 = i ^ n→i(#oc(i, ints0)) * Π(ints0 -l i) ⊦ i0 = 0, Π ints0 = i0 ^ n→i(#oc(i0, ints0)) * Π(ints0 -l i0)

Rule argument

Additional information

Used simplifier rules: eq-nonzero: ⊦ i ≠ 0 → (i * j = i * j0 ↔ j = j0); from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%neq-not-zero: ⊦ i * j ≠ i * j0 → i ≠ 0; (forward) from specification int-mult%nat2int: ⊦ 0 ≤ n→i(n); from specification intnat%mone-06: ⊦ ~1 < i ↔ 0 ≤ i; from specification int-abs%numls-02: ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0; from specification int-abs%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%pred: ⊦ (i + 1)-1 = i; from specification int-basic2