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Proof step 3 from proof perm-unique (previous step)

∀ ay. perm(ax0, ay) ∧ unique_al(ax0) ∧ perm(ay, ax0) → unique_al(ay) ⊦ perm(p + ax0, ay) ∧ unique_al(p + ax0) ∧ perm(ay, p + ax0) → unique_al(ay)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1;% ⊦ 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)% ⊦ p + ax = p ' + ax;