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Proof step 29 from proof rm-allsize (previous step)

rmdup(z) = y + a ' + z0, a ∈ z, (∀ a. a ∈ x0 ↔ a ∈ (y0 + y) + z0) → # rmdup(x0) = # rmdup((y0 + y) + z0), ∀ a0. a0 ≠ a → (a0 ∈ x0 ↔ a0 ∈ y0 ∨ a0 ∈ z) ⊦ # rmdup(x0) = # rmdup((y0 + y) + z0), a ∈ y0, a ∈ x0, a ∈ y, a ∈ z0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 30:
rmdup(z) = y + a ' + z0, a ∈ z, ∀ a0. a0 ≠ a → (a0 ∈ x0 ↔ a0 ∈ y0 ∨ a0 ∈ z) ⊦ # rmdup(x0) = # rmdup((y0 + y) + z0), a0 ∈ x0 ↔ a0 ∈ y0 ∨ a0 ∈ y ∨ a0 ∈ z0, a ∈ y0, a ∈ x0, a ∈ y, a ∈ z0

Rule argument

Additional information

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