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Proof step 2 from proof rm-size (previous step)

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

User applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ a, y. # rmdup(x0 + a ' + y) = # rmdup(x0 + y) + 1 ∨ a ∈ y ∨ a ∈ x0 ⊦ # 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 [], +;;%Nil: ⊦ [] + x = x; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%c: ⊦ a + x = a ' + x; from specification list%len-05: ⊦ #(a ' + x) = (# x)+1; from specification list%succ: ⊦ m +1 = m + 1; from specification nat-basic2%eq-01: ⊦ m + n = m + n0 ↔ n = n0; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2