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Proof step 5 from proof perm-unique (previous step)

⊦ perm((a × d)' + ax0, ay) ∧ perm(ay, (a × d)' + ax0) ∧ unique_al((a × d)' + ax0) ∧ (∀ ay. perm(ax0, ay) ∧ unique_al(ax0) ∧ perm(ay, ax0) → unique_al(ay)) → unique_al(ay)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
perm((a × d)' + ax0, ay), perm(ay, (a × d)' + ax0), unique_al(ax0), ∀ ay0. perm(ay0, ax0) ∧ perm(ax0, ay0) → unique_al(ay0) ⊦ a ∈ ax0, unique_al(ay)

Rule argument

Additional information

Used simplifier rules: cons: ⊦ unique_al((a × d)' + ax) ↔ ¬ a ∈ ax ∧ unique_al(ax);% ⊦ perm(ax, ax);% ⊦ perm(ax + ax0, ax + ax1) ↔ perm(ax0, ax1);% ⊦ perm(ax, ax0) ∧ perm(ax0, ax1) → perm(ax, ax1); (forward)% ⊦ perm(ax, ax0) → perm(ax0, ax); (forward)% ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1;