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Proof step 9 from proof at-last (previous step)

∀ m. # x0 = m + 1 → x0[m] = x0.last ⊦ (a ' + x0)[# x0] = x0.last, x0 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ x ≠ [] ∧ n ≠ 0 → x[n] = x.tail[n - 1]
Proof step 11:
∀ m. # x0 = m + 1 → x0[m] = x0.last ⊦ # x0 = 0, a ' + x0 = [], (a ' + x0).tail[# x0 - 1] = x0.last, x0 = []

Rule argument

spec: <toplevel> name: get-rec seq: ⊦ x ≠ [] ∧ n ≠ 0 → x[n] = x.tail[n - 1] subst: [n, x] → [# x0, a ' + x0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # x = 0 ↔ x = []; (s)% ⊦ x + y = [] ↔ x = [] ∧ y = []; (as)% ⊦ a ' ≠ []; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list Used terms: # x0, a ' + x0