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Proof step 4 from proof lookup-append-01 (previous step)

∀ ay, a. (ax0 + ay)[a] = ay[a] ∨ a ∈ ax0 ⊦ ((p ' + ax0) + ay)[a] = ay[a], a ∈ p ', a ∈ ax0

User applied rule structural induction

And obtained the following new goals

Proof step 5:
⊦ (∀ ay, a. (ax0 + ay)[a] = ay[a] ∨ a ∈ ax0) → (((a × d)' + ax0) + ay)[a0] = ay[a0] ∨ a0 ∈ (a × d)' ∨ a0 ∈ ax0

Rule argument

indvar: p

Additional information

Used simplifier rules: pair freely generated by ×;;