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Proof step 17 from proof nodups-butlastn (previous step)

∀ a, n. a ∈ butlastn(n, x) ∧ n ≤ # x → a ∈ x, a ∈ butlastn(n, a0 + x), n ≤ #(a0 + x) ⊦ a ∈ a0 + x

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
a ∈ butlastn(n, a0 ' + x), n ≤ # x + 1, ∀ a, n. a ∈ butlastn(n, x) ∧ n ≤ # x → a ∈ x ⊦ a = a0, a ∈ x

Rule argument

Additional information

Used simplifier rules: in-06: ⊦ ¬ a ∈ b ' + x ↔ a ≠ b ∧ ¬ a ∈ x; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%succ: ⊦ m +1 = m + 1; from specification nat-basic2%len-05: ⊦ #(a ' + x) = (# x)+1; from specification list%c: ⊦ a + x = a ' + x; from specification list