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

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

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), ∀ a, d. a ∈ ax0 ∨ unique_al(ax0 + (a × d)') ⊦ a = a0, a ∈ ax0, ¬ a0 ∈ ax0 + (a × d)' ∧ unique_al(ax0 + (a × d)'), a0 ∈ ax0

Rule argument

name: cons rotate: F subst: [ax, d, a] → [ax0 + (a × d)', d0, a0]

Additional information

Used simplifier rules: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; Used terms: ax0 + (a × d)', d0, a0