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Proof step 16 from proof product-pot-no-dups (previous step)

j ^ n→i(# rmdup(i0 ' + ints1)) < i0 ^ (1 + n→i(#oc(i0, ints1))) * Π(ints1 -l i0), 0 < min(i0 ' + ints1), i0 ^ (1 + n→i(#oc(i0, ints1))) ≤ j, 0 < i0, i ∈ ints1 → 0 < i ∧ i ^ (n→i(#oc(i, i0 ')) + n→i(#oc(i, ints1))) ≤ j, ∀ i. i ∈ ints1 → 0 < i ∧ i ^ (n→i(#oc(i, i0 ')) + n→i(#oc(i, ints1))) ≤ j, ∀ ints0, j. # ints0 < #(i0 + ints1) → j ^ n→i(# rmdup(ints0)) < Π ints0 ∧ (∀ i. i ∈ ints0 → 0 < i ∧ i ^ n→i(#oc(i, ints0)) ≤ j) → false ⊦ j ^ n→i(# rmdup(ints1 -l i0)) < Π(ints1 -l i0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
j ^ n→i(# rmdup(i0 ' + ints1)) < i0 ^ (1 + n→i(#oc(i0, ints1))) * Π(ints1 -l i0), 0 < min(i0 ' + ints1), i0 ^ (1 + n→i(#oc(i0, ints1))) ≤ j, 0 < i0, Π(ints1 -l i0) ≤ j ^ n→i(# rmdup(ints1 -l i0)), i ∈ ints1 → 0 < i ∧ i ^ (n→i(#oc(i, i0 ')) + n→i(#oc(i, ints1))) ≤ j, ∀ i. i ∈ ints1 → 0 < i ∧ i ^ (n→i(#oc(i, i0 ')) + n→i(#oc(i, ints1))) ≤ j, ∀ ints0, j. # ints0 < #(i0 + ints1) → 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: lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs