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Proof step 3 from proof rmpos-get (previous step)

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

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 4:
m < #(a + x0), n + 1 < #(a + x0), ∀ n, m. n + 1 < # x0 ∧ m < # x0 → (x0 -p m)[n] = (n < m ⊃ x0[n];x0.tail[n]) ∨ x0 = [] ⊦ a + x0 = [], ((a + x0) -p m)[n] = (n < m ⊃ (a + x0)[n];(a + x0).tail[n])

Rule argument

term: x

Additional information

Used simplifier rules: list freely generated by [], +;;