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Proof step 8 from proof get-finto (previous step)

¬ m < # a ', n0 ≤ # x0, m ≤ n0, m ≤ # x0, ∀ m, x0, a. m ≤ # x0 ∧ n0 ≤ # x0 + 1 ∧ m < n0 ∧ (∀ m, n. m < n ∧ n ≤ # x0 ∧ m < # x0 → (x0 to n)[m] = x0[m] ∨ n = 0 ∨ x0 = []) → (a ' + x0 to n0)[m] = (a ' + x0)[m] ∨ n0 = 0, ∀ m, n. m < n ∧ n ≤ # x0 ∧ m < # x0 → (x0 to n)[m] = x0[m] ∨ n = 0 ∨ x0 = [] ⊦ (a ' + (x0 to n0))[m] = x0[m - # a ']

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
n0 ≤ # x0, m ≤ n0, m ≤ # x0, ∀ m, x0, a. m ≤ # x0 ∧ n0 ≤ # x0 + 1 ∧ m < n0 ∧ (∀ m, n. m < n ∧ n ≤ # x0 ∧ m < # x0 → (x0 to n)[m] = x0[m] ∨ n = 0 ∨ x0 = []) → (a ' + x0 to n0)[m] = (a ' + x0)[m] ∨ n0 = 0, ∀ m, n. m < n ∧ n ≤ # x0 ∧ m < # x0 → (x0 to n)[m] = x0[m] ∨ n = 0 ∨ x0 = [] ⊦ (x0 to n0)[m - 1] = x0[m - 1], m = 0

Rule argument

Additional information

Used simplifier rules: one-01: ⊦ m < 1 ↔ m = 0; from specification nat-basic1%a: ⊦ (x + y) + z = x + y + z; from specification list%len-02: ⊦ # a ' = 0 +1; from specification list%get-append-grt: ⊦ ¬ n < # x → (x + y)[n] = y[n - # x]; from specification list-del