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Proof step 6 from proof unique-add (previous step)

∀ a, d. unique_al(ax0) → a ∈ ax0 ∨ unique_al(ax0 + (a × d)'), unique_al(p + ax0) ⊦ a ∈ p + ax0, unique_al((p + ax0) + (a × d)')

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
unique_al(p ' + ax0), unique_al(ax0), ∀ a, d. a ∈ ax0 ∨ unique_al(ax0 + (a × d)') ⊦ a ∈ p ', a ∈ ax0, unique_al((p ' + ax0) + (a × d)')

Rule argument

Additional information

Used simplifier rules: in-append: ⊦ a ∈ ax + ay ↔ a ∈ ax ∨ a ∈ ay;%not: ⊦ ¬ unique_al(ax) → ¬ unique_al(p ' + ax);% ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1;% ⊦ p + ax = p ' + ax;