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Proof step 14 from proof lenle (previous step)

# ay0 + # az < # ax0, unique_al(ax0.tail), ∀ a0. a0 ∈ ax0 → a0 ∈ ay0 ∨ a0 ∈ az ⊦ ax0 = [], a ∈ ax0, ax0.head.1 ∈ ax0.tail, #(ay0 + az) < # ax0 ∧ (∀ a. a ∈ ax0 → a ∈ ay0 + az)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
# ay0 + # az < # ax0, unique_al(ax0.tail), a0 ∈ ax0, ∀ a0. a0 ∈ ax0 → a0 ∈ ay0 ∨ a0 ∈ az ⊦ ax0 = [], ax0.head.1 ∈ ax0.tail, a ∈ ax0, a0 ∈ ay0, a0 ∈ az

Rule argument

Additional information

Used simplifier rules: inapp: ⊦ a ∈ ax + ay ↔ a ∈ ax ∨ a ∈ ay;%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[assoclist]% ⊦ #(ax + ax0) = # ax + # ax0; (s)