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Proof step 8 from proof at-last (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ x ≠ [] ∧ n ≠ 0 → x[n] = x.rest[n - 1]
Proof step 10:
a ' + x0 ≠ [] ∧ # x0 ≠ 0, ∀ m. # x0 = m + 1 → x0[m] = x0.last ⊦ x0 = [], (a ' + x0).rest[# x0 - 1] = x0.last

Rule argument

spec: list-del inst: name: get-rec seq: ⊦ x ≠ [] ∧ n ≠ 0 → x[n] = x.rest[n - 1] subst: [n, x] → [# x0, a ' + x0] flags: rewrite, current

Additional information

Used simplifier rules: e-01: ⊦ a ' + x ≠ []; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%l: ⊦ # x = 0 ↔ x = []; from specification list-data Used terms: # x0, a ' + x0