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Proof step 3 from proof lenle (previous step)

∀ ay. # ay < # ax0 ∧ unique_al(ax0) ∧ (∀ a. a ∈ ax0 → a ∈ ay) → ax0 = [] ⊦ # ay < #(p + ax0) ∧ unique_al(p + ax0) ∧ (∀ a. a ∈ p + ax0 → a ∈ ay) → p + ax0 = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
# ay ≤ # ax0, unique_al(p ' + ax0), unique_al(ax0) ∧ (∃ ay0. (∀ a. a ∈ ax0 → a ∈ ay0) ∧ ¬ # ax0 ≤ # ay0) → ax0 = [], ∀ a. a ∈ p ' ∨ a ∈ ax0 → a ∈ ay ⊦

Rule argument

Additional information

Used simplifier rules: inapp: ⊦ a ∈ ax + ay ↔ ¬ ¬(a ∈ ax ∨ a ∈ ay);% ⊦ ¬ m < n ↔ n ≤ m;% ⊦ m < n + 1 ↔ ¬ n < m;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ n + 0 = n;% ⊦ m +1 = m + 1;% ⊦ # p ' = 0 +1;% ⊦ #(ax + ax0) = # ax + # ax0;% ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1;% ⊦ p ' + ax ≠ [];% ⊦ p + ax = p ' + ax;