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Proof step 4 from proof diffgetn-nodupssize (previous step)

# x = m + 1, n ≤ m ⊦ #(x \ x[n] ') = m, x = [], dups(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 \ x0[n] ') = m ∨ x0 = [] ∨ dups(x0), #(a + x0) = m + 1, n ≤ m ⊦ #((a + x0) \ (a + x0)[n] ') = m, a + x0 = [], dups(a + x0)

Rule argument

term: x

Additional information

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