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Proof step 8 from proof lastN-blastN (previous step)

n ≤ # x, x ≠ [] → x = y + a ', ∀ x0, n. # x0 < # x → n ≤ # x0 → butlastn(n, x0) + lastn(n, x0) = x0 ⊦ butlastn(n, x) + lastn(n, x) = x, x = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
n ≤ # y + 1, ∀ x0, n. # x0 < #(y + a ') → n ≤ # x0 → butlastn(n, x0) + lastn(n, x0) = x0 ⊦ butlastn(n, y + a ') + lastn(n, y + a ') = y + a '

Rule argument

Additional information

Used simplifier rules: ⊦ # a ' = 0 +1; (s)% ⊦ #(x + y) = # x + # y; (s)% ⊦ a ∈ b ' ↔ a = b; (s)% ⊦ a ∈ x + y ↔ a ∈ x ∨ a ∈ y; (s)% ⊦ x + a ' ≠ []; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list%in-15: ⊦ x + a ' = y → a ∈ y; (forward) from specification list