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Proof step 8 from proof perm-unique (previous step)

a × d ∈ ay ∧ perm(ax0, ay -1l (a × d)), perm(ay, (a × d)' + ax0), unique_al(ax0), ∀ ay0. perm(ay0, ax0) ∧ perm(ax0, ay0) → unique_al(ay0) ⊦ a ∈ ax0, unique_al(ay)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
perm(ax0, ay -1l (a × d)), a × d ∈ ay, perm(ay, (a × d)' + ax0), unique_al(ax0), perm(ay -1l (a × d), ax0), ∀ ay0. perm(ay0, ax0) ∧ perm(ax0, ay0) → unique_al(ay0) ⊦ a ∈ ax0, unique_al(ay)

Rule argument

Additional information

Used simplifier rules: ⊦ perm(ax, ax);% ⊦ perm(ax, ax0) ∧ perm(ax0, ax1) → perm(ax, ax1); (forward)% ⊦ perm(ax, ax0) → perm(ax0, ax); (forward)