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Proof step 8 from proof put-at (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
∀ m, n, a. m < # x0 → m ≠ n → x0[m, a][n] = x0[n] ⊦ n = 0, x0[n - 1] = (a0 ' + x0)[n]

Rule argument

Additional information

Used simplifier rules: e-01: ⊦ a ' + x ≠ []; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%c-07: ⊦ (a ' + x).rest = x; from specification list