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Proof step 3 from proof unique-02 (previous step)

unique_al(ax), a × d0 ∈ ax, a × d ∈ ax ⊦ d = d0

User applied rule structural induction

And obtained the following new goals

Proof step 4:
unique_al(p + ax0), a × d ∈ p + ax0, a × d0 ∈ p + ax0, ∀ a, d0, d. unique_al(ax0) ∧ a × d0 ∈ ax0 ∧ a × d ∈ ax0 → d = d0 ⊦ d = d0

Rule argument

indvar: ax

Additional information

Used simplifier rules: assoclist freely generated by [], +;;% ⊦ ¬ p ∈ []; (s)