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Proof step 9 from proof blastN-rec-01 (previous step)

n ≤ # y + 1, ∀ x0, n, a. # x0 < #(y + a0 ') → n ≤ # x0 → butlastn(n, a ' + x0) = a ' + butlastn(n, x0) ⊦ n = 0, butlastn(n, a ' + y + a0 ') = a ' + butlastn(n, y + a0 ')

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ n ≠ 0 → butlastn(n, x + a ') = butlastn(n -1, x)
Proof step 11:
n ≠ 0, n ≤ # y + 1, ∀ x0, n, a. # x0 < #(y + a0 ') → n ≤ # x0 → butlastn(n, a ' + x0) = a ' + butlastn(n, x0) ⊦ n = 0, butlastn(n -1, a ' + y) = a ' + butlastn(n, y + a0 ')

Rule argument

spec: list-last inst: name: blastN-rec seq: ⊦ n ≠ 0 → butlastn(n, x + a ') = butlastn(n -1, x) subst: [a, x, n] → [a0, a ' + y, n] flags: rewrite, current

Additional information

Used simplifier rules: a: ⊦ (x + y) + z = x + y + z; from specification list Used terms: a0, a ' + y, n