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Proof step 28 from proof product-pot-no-dups (previous step)

¬(j ^ n→i(# rmdup(i0 ' + ints1)) < j * Π(ints1 -l i0) ∧ Π(ints1 -l i0) ≤ j ^ n→i(# rmdup(ints1 -l i0)) ∧ 0 ≤ j), 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 ⊦ j ^ n→i(# rmdup(i0 ' + ints1)) < j * j ^ n→i(# rmdup(ints1 -l i0))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%ls-forward: ⊦ i * j < i * j0 → i ≠ 0; (forward) from specification int-mult%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%notneg-02: ⊦ 0 < i → ¬ i ^ j < 0; from specification int-pot%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%transitivity: ⊦ i < i0 ∧ i0 < i1 → i < i1; (forward) from specification oelem[intlista]%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs