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Proof step 16 from proof perm-unique (previous step)

perm(ax0, ay -1l (a × d)), a × d ∈ ay, perm(ay, (a × d)' + ax0), unique_al(ax0), perm(ay -1l (a × d), ax0), unique_al(ay -1l (a × d)), ∃ d0. a × d0 ∈ ay -1l (a × d) ⊦ a ∈ ax0, unique_al(ay)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
a × d0 ∈ ay, a × d0 ∈ ay -1l (a × d), unique_al(ay -1l (a × d)), perm(ay -1l (a × d), ax0), unique_al(ax0), perm(ay, (a × d)' + ax0), a × d ∈ ay, perm(ax0, ay -1l (a × d)) ⊦ unique_al(ay), a ∈ ax0

Rule argument

Additional information

Used simplifier rules: unique-02: ⊦ unique_al(ax) ∧ a × d ∈ ax ∧ a × d0 ∈ ax → d = d0;% ⊦ p ∈ ax -1l p0 → p ∈ ax; (forward)