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

∀ 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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
∀ 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 = a0, a ∈ y, a ∈ x0

Rule argument

Additional information

Used simplifier rules: in-06: ⊦ ¬ a ∈ b ' + x ↔ a ≠ b ∧ ¬ a ∈ x; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%c: ⊦ a + x = a ' + x; from specification list