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Proof step 6 from proof lenle (previous step)

# ay ≤ # ax0, unique_al(ax0), (∃ ay0. (∀ a. a ∈ ax0 → a ∈ ay0) ∧ ¬ # ax0 ≤ # ay0) → ax0 = [], ∀ a0. a0 ∈ ax0 ∨ a0 = a → a0 ∈ ay ⊦ a ∈ ax0

User applied rule cut formula

And obtained the following new goals

Proof step 7:
# ay ≤ # ax0, unique_al(ax0), (∃ ay0. (∀ a. a ∈ ax0 → a ∈ ay0) ∧ ¬ # ax0 ≤ # ay0) → ax0 = [], ∀ a0. a0 ∈ ax0 ∨ a0 = a → a0 ∈ ay ⊦ ax0 = [], a ∈ ax0

Rule argument

fma: ax0 = []

Additional information

Used simplifier rules: unique-e: ⊦ unique_al([]);%empty: ⊦ ¬ a ∈ [];% ⊦ # [] = 0;% ⊦ m ≤ 0 ↔ m = 0;% ⊦ # ax = 0 ↔ ax = [];% ⊦ 0 ≤ m; Used formulas: ax0 = []