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Proof step 8 from proof unique-add (previous step)

unique_al((a0 × d0)' + ax0), unique_al(ax0), ∀ a, d. a ∈ ax0 ∨ unique_al(ax0 + (a × d)') ⊦ a ∈ (a0 × d0)', a ∈ ax0, unique_al(((a0 × d0)' + ax0) + (a × d)')

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
unique_al(ax0), ∀ a, d. a ∈ ax0 ∨ unique_al(ax0 + (a × d)') ⊦ a = a0, a ∈ ax0, unique_al(((a0 × d0)' + ax0) + (a × d)'), a0 ∈ ax0

Rule argument

Additional information

Used simplifier rules: cons: ⊦ unique_al((a × d)' + ax) ↔ ¬ a ∈ ax ∧ unique_al(ax);%inone: ⊦ a ∈ (b × d0)' ↔ a = b;% ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1;