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Proof step 6 from proof perm-unique (previous step)

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)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ perm(p ' + ax, ax0) ↔ ¬ ¬(p ∈ ax0 ∧ perm(ax, ax0 -1l p))
Proof step 8:
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)

Rule argument

seq: ⊦ perm(p ' + ax, ax0) ↔ ¬ ¬(p ∈ ax0 ∧ perm(ax, ax0 -1l p)) subst: [ax0, ax, p] → [ay, ax0, a × d] rotate: F spec: list-perm inst: assoclista name: del-01

Additional information

Used terms: ay, ax0, a × d