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Proof step 9 from proof unique-del (previous step)

unique_al(ax0 -1l (a0 × d0)), ∀ a, d. unique_al(ax0 -1l (a × d)) → a ∈ ax0 -1l (a × d) ∨ unique_al(ax0) ⊦ a0 × d0 = a × d, a0 = a, a ∈ ax0 -1l (a0 × d0), unique_al((a × d)' + ax0), a0 ∈ ax0 -1l (a0 × d0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ unique_al((a × d)' + ax) ↔ ¬ a ∈ ax ∧ unique_al(ax)
Proof step 11:
unique_al(ax0 -1l (a0 × d0)), ∀ a, d. unique_al(ax0 -1l (a × d)) → a ∈ ax0 -1l (a × d) ∨ unique_al(ax0) ⊦ a0 × d0 = a × d, a0 = a, a ∈ ax0 -1l (a0 × d0), ¬ a ∈ ax0 ∧ unique_al(ax0), a0 ∈ ax0 -1l (a0 × d0)

Rule argument

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

Additional information

Used terms: ax0, d, a