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Proof step 8 from proof get-last-04 (previous step)

# x = m + 1 ⊦ x = [], (x + y)[m] = x.last

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ n < # x → (x + y)[n] = x[n]
Proof step 10:
m < # x, # x = m + 1 ⊦ x = [], x[m] = x.last

Rule argument

spec: list-del inst: name: get-append-less seq: ⊦ n < # x → (x + y)[n] = x[n] subst: [n, y, x] → [m, y, x] flags: rewrite, current

Additional information

Used simplifier rules: lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%eq: ⊦ m = n + 1 → ¬ m ≤ n; from specification nat Used terms: m, y, x