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Proof step 2 from proof lenequal (previous step)

# ax = # ay, unique_al(ay), unique_al(ax), b ∈ ay, ∀ a. a ∈ ax → a ∈ ay ⊦ b ∈ ax

User applied rule structural induction

And obtained the following new goals

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

Rule argument

indvar: ax

Additional information

Used simplifier rules: assoclist freely generated by [], +;;% ⊦ # [] = 0; (s)% ⊦ # ax = 0 ↔ ax = []; (s)