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Proof step 32 from proof product-pot-no-dups (previous step)

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 ⊦

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 3 terms: min(ints)

Additional information

Used simplifier rules: min-in: ⊦ min(ints) ∈ ints ↔ ints ≠ []; from specification intlist%lenls: ⊦ i ≤ j → ¬ j < i; from specification int-abs%min-empty: ⊦ min([]) = 0; from specification intlist%rmdup-e: ⊦ rmdup([]) = []; from specification list-dup[intlista]%size-01: ⊦ # [] = 0; from specification list-data[intlista]%Pot-zero: ⊦ j ^ 0 = 1; from specification int-pot%prod-empty: ⊦ Π [] = 1; from specification intlist Used terms: min(ints)