>>11078374Here's how you prove it for a general group
c has an inverse, call it d.
a+c=b+c so
By closure we can add d to either side and get valid elements, and by the axioms of equality the results will equal each other.
(a+c)+d=(b+c)+d
Now left side is equal to
(a+c)+d =[by associativity] = a+(c+d) = [property of inverse] = a+0 = [property of 0] = a
Right side can similarly be shown to equal b
Hence a=b.
