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Proof step 31 from proof product-pot-no-dups (previous step)

j ^ n→i(# rmdup(ints)) < Π ints, ∀ i. i ∈ ints → 0 < i ∧ i ^ n→i(#oc(i, ints)) ≤ j, ∀ ints0, j. # ints0 < # ints → j ^ n→i(# rmdup(ints0)) < Π ints0 ∧ (∀ i. i ∈ ints0 → 0 < i ∧ i ^ n→i(#oc(i, ints0)) ≤ j) → false ⊦ 0 < min(ints)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 32:
j ^ n→i(# rmdup(ints)) < Π ints, min(ints) ≤ 0, ∀ i. i ∈ ints → 0 < i ∧ i ^ n→i(#oc(i, ints)) ≤ j, ∀ ints0, j. # ints0 < # ints → j ^ n→i(# rmdup(ints0)) < Π ints0 ∧ (∀ i. i ∈ ints0 → 0 < i ∧ i ^ n→i(#oc(i, ints0)) ≤ j) → false ⊦

Rule argument

Additional information

Used simplifier rules: forward-le-04: ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward) from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs