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Proof step 2 from proof product-all-elems-le (previous step)

i0 ^ n→i(# ints) < Π ints, ∀ i. i ∈ ints → 0 < i ∧ i ≤ i0 ⊦

User applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ i0. ¬(i0 ^ n→i(# ints0) < Π ints0 ∧ (∀ i. i ∈ ints0 → 0 < i ∧ i ≤ i0)), i0 ^ n→i(#(i + ints0)) < Π(i + ints0), ∀ i1. i1 ∈ i + ints0 → 0 < i1 ∧ i1 ≤ i0 ⊦

Rule argument

indvar: ints

Additional information

Used simplifier rules: intlist freely generated by [], +;;%size-01: ⊦ # [] = 0; from specification list-data[intlista]%Pot-zero: ⊦ j ^ 0 = 1; from specification int-pot%prod-empty: ⊦ Π [] = 1; from specification intlist