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Proof step 4 from proof lenequal (previous step)

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

User applied rule structural induction

And obtained the following new goals

Proof step 5:
1 + # ax0 = # ay, unique_al((a × d)' + ax0), unique_al(ay), b ∈ ay, ∀ a0. a0 ∈ (a × d)' ∨ a0 ∈ ax0 → a0 ∈ ay, ∀ ay, b. # ax0 = # ay ∧ unique_al(ay) ∧ unique_al(ax0) ∧ b ∈ ay ∧ (∀ a. a ∈ ax0 → a ∈ ay) → b ∈ ax0 ⊦ b ∈ ax0, b ∈ (a × d)'

Rule argument

indvar: p

Additional information

Used simplifier rules: pair freely generated by ×;;