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Proof step 2 from proof rmpos-get (previous step)

n + 1 < # x, m < # x ⊦ (x -p m)[n] = (n < m ⊃ x[n];x[n + 1])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
n + 1 < # x, m < # x ⊦ (x -p m)[n] = (n < m ⊃ x[n];x.tail[n]), x = []

Rule argument

Additional information

Used simplifier rules: get-rec-01: ⊦ x ≠ [] → x[n + 1] = x.tail[n];%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ # x = 0 ↔ x = []; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic