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Proof step 2 from proof lenequal (previous step)

∀ ay, b. unique_al(ax0) ∧ unique_al(ay) ∧ # ax0 = # ay ∧ (∀ a. a ∈ ax0 → a ∈ ay) ∧ b ∈ ay → b ∈ ax0 ⊦ unique_al(p + ax0) ∧ unique_al(ay) ∧ #(p + ax0) = # ay ∧ (∀ a. a ∈ p + ax0 → a ∈ ay) ∧ b ∈ ay → b ∈ p + ax0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
1 + # ax0 = # ay, unique_al(ay), b ∈ ay, unique_al(p ' + ax0), ∀ ay, b. unique_al(ax0) ∧ unique_al(ay) ∧ # ax0 = # ay ∧ (∀ a. a ∈ ax0 → a ∈ ay) ∧ b ∈ ay → b ∈ ax0, ∀ a. a ∈ p ' ∨ a ∈ ax0 → a ∈ ay ⊦ b ∈ ax0, b ∈ p '

Rule argument

Additional information

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