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Proof step 8 from proof extensionality (previous step)

# x = # x0, ∀ n. n < # x0 → x[n] = x0[n] ⊦ # x = # x0 ∧ (∀ n. n < # x → x[n] = x0[n])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
# x = # x0, n < # x0, ∀ n. n < # x0 → x[n] = x0[n] ⊦ x[n] = x0[n], x0 = []

Rule argument

Additional information

Used simplifier rules: l: ⊦ # x = 0 ↔ x = []; from specification list-data%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic1%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1