Theorem:
To prove :all numbers are equal.
Proof: Choose arbitrary x and y, xnd let t = x + y. Then

x + y = t
(x + y)(x - y) = t(x - y)
x^2 - y^2 = tx - ty
x^2 - tx = y^2 - ty
x^2 - tx + (t^2)/4 = y^2 - ty + (t^2)/4
(x - t/2)^2 = (y - t/2)^2
x - t/2 = y - t/2
x = y