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Proof step 3 from proof rm-size (previous step)

⊦ # rmdup(x + a ' + y) = # rmdup(x + y) + 1, a ∈ x, a ∈ y

User applied rule structural induction

And obtained the following new goals

Proof step 4:
∀ a, y. # rmdup(x0 + a ' + y) = # rmdup(x0 + y) + 1 ∨ a ∈ x0 ∨ a ∈ y ⊦ # rmdup((a0 + x0) + a ' + y) = # rmdup((a0 + x0) + y) + 1, a ∈ y, a ∈ a0 + x0

Rule argument

indvar: x

Additional information

Used simplifier rules: rmdup-n: ⊦ ¬ a ∈ x → rmdup(a ' + x) = a + rmdup(x);%list freely generated by [], +;;% ⊦ [] + x = x; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ a + x = a ' + x; (s)% ⊦ #(x + y) = # x + # y; (s)% ⊦ # a ' = 0 +1; (s)% ⊦ m + n = m + n0 ↔ n = n0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic