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Proof step 14 from proof lenle (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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

Rule argument

Additional information

Used simplifier rules: inapp: ⊦ a ∈ ax + ay ↔ ¬ ¬(a ∈ ax ∨ a ∈ ay);% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ ¬ n < n;% ⊦ m < n ∧ n ≤ n0 → m < n0; (forward)% ⊦ m ≤ n ∧ n < n0 → m < n0; (forward)% ⊦ #(ax + ax0) = # ax + # ax0;% ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1;% ⊦ m + n = n + m;