Consider the following signature:
?Function symbols: zero (arity 0); succ (arity 1)
?Predicate symbols: < (arity 2)
We will use infix notation for the binary symbol <. Consider the following formulas
that capture properties of the above symbols:
?let S1 be ?y.(?x.x < y) ?0 < y
?let S2 be ?x.x < succ(x)
For simplicity we write 0 for zero, 1 for succ(zero), 2 for succ(succ(zero)), etc.
(i) Provide a constructive Natural Deduction proof of:
S1 ?S2 ?0 < 2
(Hint: you can prove this formula without [?I] and [?E].)