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Proof step 7 from proof unique-put (previous step)

∀ a, d. unique_al(ax0[a, d]) ↔ unique_al(ax0) ⊦ a = a0, ¬ a0 ∈ ax0 ∧ unique_al(ax0[a, d]) ↔ unique_al((a0 × d0)' + ax0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ unique_al((a × d)' + ax) ↔ ¬ a ∈ ax ∧ unique_al(ax)
Proof step 9:
∀ a, d. unique_al(ax0[a, d]) ↔ unique_al(ax0) ⊦ a = a0, ¬ a0 ∈ ax0 ∧ unique_al(ax0[a, d]) ↔ ¬ a0 ∈ ax0 ∧ unique_al(ax0)

Rule argument

name: cons rotate: F subst: [ax, d, a] → [ax0, d0, a0]

Additional information

Used terms: ax0, d0, a0