16

Mouctar Diallo

16. (Preliminary for Th, Feb 22; finalized Sat, March 3) Using only results proven in class or assigned earlier (i.e., don't use induction), show that for all natural numbers x,y, if y<Succ(x), then y≤x.

work explanation
y < succ(x) given
y ε succ(x) definition of "<"
y ε U {x,{x}} definition of succ(x)
(y ε x) V (y=x) definition of inclusion
(y < x) V (y=x) definition of "<"
(y ≤ x) definition of "≤"
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