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Proof step 5 from proof at-put (previous step)

∀ a, b, d. a = b ∨ ax0[b, d][a] = ax0[a] ⊦ a = b, (p ' + ax0)[b, d][a] = (p ' + ax0)[a]

User applied rule structural induction

And obtained the following new goals

Proof step 6:
∀ a, b, d. a = b ∨ ax0[b, d][a] = ax0[a] ⊦ a = b, ((a0 × d0)' + ax0)[b, d][a] = ((a0 × d0)' + ax0)[a]

Rule argument

indvar: p

Additional information

Used simplifier rules: pair freely generated by ×;;