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Proof step 9 from proof put-at (previous step)

∀ m, a, n. m < # x0 → x0[m, a][n] = x0[n] ∨ m = n ⊦ a0 ' + x0 = [], a ' + x0 = [], (a ' + x0).tail[n - 1] = (a0 ' + x0)[n], n = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
∀ m, a, n. m < # x0 → x0[m, a][n] = x0[n] ∨ m = n ⊦ x0[n - 1] = (a0 ' + x0)[n], n = 0

Rule argument

Additional information

Used simplifier rules: ⊦ a ' + x ≠ []; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ (a ' + x).tail = x; (s)