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Proof step 6 from proof lookup-02 (previous step)

unique_al(ax0), unique_al(p ' + ax0), a × d ∈ ax0, ∀ a0, d0. a0 × d0 ∈ ax0 → ax0[a0] = d0 ⊦ (p ' + ax0)[a] = d, a × d = p

User applied rule structural induction

And obtained the following new goals

Proof step 7:
⊦ unique_al(ax0) ∧ unique_al((a × d)' + ax0) ∧ a0 × d0 ∈ ax0 ∧ (∀ a0, d0. a0 × d0 ∈ ax0 → ax0[a0] = d0) → ((a × d)' + ax0)[a0] = d0 ∨ a0 × d0 = a × d

Rule argument

indvar: p

Additional information

Used simplifier rules: pair freely generated by ×;;