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Proof step 4 from proof l (previous step)

# x = m + 1, a ∈ x ⊦ #(x -1l a) = m, x = []

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 5:
∀ m, a. # x0 = m + 1 ∧ a ∈ x0 → #(x0 -1l a) = m ∨ x0 = [], #(a0 + x0) = m + 1, a ∈ a0 + x0 ⊦ #((a0 + x0) -1l a) = m, a0 + x0 = []

Rule argument

term: x

Additional information

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