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Proof step 5 from proof unique (previous step)

∀ a, d. unique_al(ax0 + (a × d)') → unique_al(ax0) ⊦ unique_al((p + ax0) + (a × d)') → unique_al(p + ax0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
unique_al((p ' + ax0) + (a × d)'), (∃ a, d. unique_al(ax0 + (a × d)')) → unique_al(ax0) ⊦ unique_al(p ' + ax0)

Rule argument

Additional information

Used simplifier rules: ⊦ p + ax = p ' + ax;