(* Goal: ``x+y == 2*y+(x-y)`` *)
alias eq        /Coq/Init/Logic/Equality/eq.ind#1/1
alias eqT       /Coq/Init/Logic_Type/eqT.ind#1/1
alias R         /Coq/Reals/Rdefinitions/R.con
alias Rplus     /Coq/Reals/Rdefinitions/Rplus.con
alias Rmult     /Coq/Reals/Rdefinitions/Rmult.con
alias R1        /Coq/Reals/Rdefinitions/R1.con
alias R0        /Coq/Reals/Rdefinitions/R0.con
alias Ropp      /Coq/Reals/Rdefinitions/Ropp.con
!x:R.!y:R.
(eqT R
  (Rplus x y)
  (Rplus (Rmult (Rplus R1 R1) y) (Rplus x (Ropp y)))
)