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Proof step 11 from proof unique-add (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
unique_al(ax0), ∀ a, d. a ∈ ax0 ∨ unique_al(ax0 + (a × d)') ⊦ a = a0, a ∈ ax0, a0 ∈ ax0, unique_al(ax0 + (a × d)')

Rule argument

Additional information

Used simplifier rules: in-append: ⊦ a ∈ ax + ay ↔ a ∈ ax ∨ a ∈ ay;%inone: ⊦ a ∈ (b × d0)' ↔ a = b;% ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1;