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Proof step 5 from proof nodups-rmposnodups (previous step)

n = n1 +1, dups((a ' + x0) -1l n), ∀ n0. ¬ dups(x0 -1l n0) ⊦ a ∈ x0, dups(x0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
∀ n0. ¬ dups(x0 -1l n0), a ∈ x0 -1l n1 ∨ dups(x0 -1l n1) ⊦ a ∈ x0, dups(x0)

Rule argument

Additional information

Used simplifier rules: delpos-rec: ⊦ (a ' + x) -1l (n + 1) = a + (x -1l n);%rec: ⊦ dups(a ' + x) ↔ ¬ ¬(a ∈ x ∨ dups(x)); from specification list-dup%a: ⊦ (x + y) + z = x + y + z; from specification list%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ a + x = a ' + x; from specification list%succ: ⊦ m +1 = m + 1; from specification nat-basic2