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Proof step 4 from proof perm-eq (previous step)

unique_al(ax), perm(ax, ay), ∃ d. a × d ∈ ax, perm(ay, ax), unique_al(ay) ⊦ ax[a] = ay[a]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
unique_al(ay), perm(ay, ax), a × d ∈ ax, perm(ax, ay), unique_al(ax) ⊦ ax[a] = ay[a]

Rule argument

Additional information

Used simplifier rules: unique-02: ⊦ unique_al(ax) ∧ a × d ∈ ax ∧ a × d0 ∈ ax → d = d0;