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Proof step 7 from proof get-butlast (previous step)

n ≤ # x0, ∀ n0, a1. n0 < # x0 → (x0 + a1 ')[n0] = x0[n0] ⊦ ((a0 ' + x0) + a ')[n] = (a0 ' + x0)[n], x0 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ x ≠ [] ∧ n ≠ 0 → x[n] = x.tail[n - 1]
Proof step 9:
n ≤ # x0, ∀ n0, a1. n0 < # x0 → (x0 + a1 ')[n0] = x0[n0] ⊦ (a0 ' + x0) + a ' = [], ((a0 ' + x0) + a ').tail[n - 1] = (a0 ' + x0)[n], n = 0, x0 = []

Rule argument

spec: <toplevel> name: get-rec seq: ⊦ x ≠ [] ∧ n ≠ 0 → x[n] = x.tail[n - 1] subst: [n, x] → [n, (a0 ' + x0) + a '] flags: <all paths>

Additional information

Used simplifier rules: get-zero-01: ⊦ (a ' + x)[0] = a;% ⊦ a ' + x ≠ []; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list Used terms: n, (a0 ' + x0) + a '