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Proof step 6 from proof unique-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
unique_al(ax0 + (a × d)'), unique_al(ax0), a ∈ ax0, ∀ a1, d0. ¬ unique_al(ax0 + (a1 × d0)') ∨ ¬ a1 ∈ ax0 ⊦ a0 ∈ ax0

Rule argument

Additional information

Used simplifier rules: cons: ⊦ unique_al((a × d)' + ax) ↔ ¬ a ∈ ax ∧ unique_al(ax);%inapp: ⊦ a ∈ ax + ay ↔ a ∈ ax ∨ a ∈ ay;%inone: ⊦ a ∈ (b × d0)' ↔ a = b;%unique: ⊦ unique_al(ax + p ') → unique_al(ax);%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[assoclist]