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Proof step 6 from proof firstN-dups-04 (previous step)

x = a + y, n0 < # x, ∀ x. dups(firstn(n0, x)) ∧ n0 ≤ # x → dups(x), a ∈ firstn(n0, y) ∨ dups(firstn(n0, y)) ⊦ x = [], dups(x)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: firstN-in: ⊦ ¬ a ∈ x ∧ n ≤ # x → ¬ a ∈ firstn(n, x);% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ dups(a ' + x) ↔ dups(x) ∨ a ∈ x; (ws)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ # a ' = 0 +1; (s)% ⊦ #(x + y) = # x + # y; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ a ' + x ≠ []; (s)% ⊦ a + x = a ' + x; (s)