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Proof step 4 from proof rmpos-size (previous step)

# x = m + 1, n ≤ m ⊦ #(x -1l n) = m, x = []

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 5:
∀ m, n. # x0 = m + 1 ∧ n ≤ m → #(x0 -1l n) = m ∨ x0 = [], #(a + x0) = m + 1, n ≤ m ⊦ #((a + x0) -1l n) = m, a + x0 = []

Rule argument

term: x

Additional information

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