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Proof step 6 from proof rm-size (previous step)

∀ a, y. # rmdup(x0 + a ' + y) = # rmdup(x0 + y) + 1 ∨ a ∈ y ∨ a ∈ x0 ⊦ # (a0 ∈ x0 + a ' + y ⊃ rmdup(x0 + a ' + y);a0 ' + rmdup(x0 + a ' + y)) = # rmdup((a0 ' + x0) + y) + 1, a = a0, a ∈ y, a ∈ x0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
∀ a, y. # rmdup(x0 + a ' + y) = # rmdup(x0 + y) + 1 ∨ a ∈ y ∨ a ∈ x0 ⊦ a = a0, # (a0 ∈ x0 ∨ a0 ∈ y ⊃ rmdup(x0 + a ' + y);a0 ' + rmdup(x0 + a ' + y)) = # rmdup((a0 ' + x0) + y) + 1, a ∈ y, a ∈ x0

Rule argument

Additional information

Used simplifier rules: a: ⊦ (x + y) + z = x + y + z; from specification list%in-01: ⊦ a ≠ b → (a ∈ b ' + x ↔ a ∈ x); from specification list%in-append: ⊦ a ∈ x + y ↔ ¬ ¬(a ∈ x ∨ a ∈ y); from specification list