Let R1 and R2 be relations on N defined by
xR1y if and only if y=a+x for some a in N0.
xR2y if and only if y=xa for some a in N.
for all x,y in N.
Also N0 denotes all integers x>=0, while N denotes all integers >= 1.
There are two different things I want to write a proof for with this.
I want to write a proof to show that R1 is a total order on N.
I want to write a proof to show that R2 is a partial order on N.
I have others I want to try and do but for now if someone could model how to do
the first one and then I can use your proof to complete my second.