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[Sa] means the successor of a.

Base Case: y = S0

x.S0 = S0

→ x.0 + x = S0

→ 0 + x = S0

→ x = S0 & y=S0

Now the induction step is usually y=a to y=Sa, however this does not work here, I assume I need to take a new y and it's successor to proceed. Would anyone know how to proceed and which y to take?

Thanks