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

n0 ≤ # x0, m ≤ n0, m ≤ # x0, ∀ m, x0, a. m < n0 ∧ m ≤ # x0 ∧ n0 ≤ 1 + # x0 ∧ (∀ m, n. m < n ∧ m < # x0 ∧ n ≤ # x0 → (x0 to n)[m] = x0[m] ∨ x0 = []) → (a ' + x0 to n0)[m] = (a ' + x0)[m], ∀ m, n. m < n ∧ m < # x0 ∧ n ≤ # x0 → (x0 to n)[m] = x0[m] ∨ x0 = [] ⊦ (a ' + (x0 to n0))[m] = (a ' + x0)[m]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ ¬ n < # x → (x + y)[n] = y[n - # x]
Proof step 9:
m ≤ # x0, m ≤ n0, n0 ≤ # x0, ∀ m, n. m < n ∧ m < # x0 ∧ n ≤ # x0 → (x0 to n)[m] = x0[m] ∨ x0 = [], ∀ m, x0, a. m < n0 ∧ m ≤ # x0 ∧ n0 ≤ 1 + # x0 ∧ (∀ m, n. m < n ∧ m < # x0 ∧ n ≤ # x0 → (x0 to n)[m] = x0[m] ∨ x0 = []) → (a ' + x0 to n0)[m] = (a ' + x0)[m] ⊦ (a ' + (x0 to n0))[m] = x0[m - # a '], m < # a '

Rule argument

spec: list-del name: get-append-grt seq: ⊦ ¬ n < # x → (x + y)[n] = y[n - # x] subst: [n, y, x] → [m, x0, a '] flags: <all paths>

Additional information

Used simplifier rules: ⊦ n < # x → (x + y)[n] = x[n]; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list Used terms: m, x0, a '