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Proof step 20 from proof dups-eqsize-02 (previous step)

# x0 = # y0 + # z, dups(y0 + a0 ' + z), ∀ y0, a1. # x0 = # y0 ∧ (∀ a. a ∈ x0 → a ∈ y0) → ¬ dups(y0) ∧ (a1 ∈ y0 → a1 ∈ x0), a1 ∈ x0 → a1 ∈ y0 ∨ a1 ∈ z, ∀ a1. a1 ∈ x0 → a1 ∈ y0 ∨ a1 ∈ z, a ∈ y0 ∨ a ∈ z → a ∈ x0 ⊦ # x0 = #(y0 + z) ∧ ¬ dups(x0) ∧ ¬ dups(y0 + z) ∧ (∀ a. a ∈ x0 → a ∈ y0 + z), a0 ∈ x0, dups(x0), dups(y0 + z), ¬ a0 ∈ y0 ∧ ¬ a0 ∈ z

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
# x0 = # y0 + # z, dups(y0 + a0 ' + z), a2 ∈ x0, ∀ y0, a1. # x0 = # y0 ∧ (∀ a. a ∈ x0 → a ∈ y0) → ¬ dups(y0) ∧ (a1 ∈ y0 → a1 ∈ x0), a1 ∈ x0 → a1 ∈ y0 ∨ a1 ∈ z, ∀ a1. a1 ∈ x0 → a1 ∈ y0 ∨ a1 ∈ z, a ∈ y0 ∨ a ∈ z → a ∈ x0 ⊦ a0 ∈ x0, dups(x0), dups(y0 + z), a2 ∈ y0, a2 ∈ z, ¬ a0 ∈ y0 ∧ ¬ a0 ∈ z

Rule argument

Additional information

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