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Proof step 10 from proof blastN-len (previous step)

# y + 1 = n0 + n, ∀ x0, n0, n. # x0 < #(y + a ') → # x0 = n0 + n → # butlastn(n, x0) = n0 ⊦ # butlastn(n, y + a ') = n0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ n ≠ 0 → butlastn(n, x + a ') = butlastn(n -1, x)
Proof step 12:
# y + 1 = n0 + n, ∀ x0, n0, n. # x0 < #(y + a ') → # x0 = n0 + n → # butlastn(n, x0) = n0 ⊦ # butlastn(n -1, y) = n0, n = 0

Rule argument

spec: <toplevel> name: blastN-rec seq: ⊦ n ≠ 0 → butlastn(n, x + a ') = butlastn(n -1, x) subst: [a, x, n] → [a, y, n] flags: <all paths>

Additional information

Used simplifier rules: butlastN-base: ⊦ butlastn(0, x) = x;% ⊦ 0 + m = m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ #(x + y) = # x + # y; (s)% ⊦ # a ' = 0 +1; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list Used terms: a, y, n