alias Rge /Coq/Reals/Rdefinitions/Rge.con
alias Rle /Coq/Reals/Rdefinitions/Rle.con
+alias Rgt /Coq/Reals/Rdefinitions/Rgt.con
+alias Rlt /Coq/Reals/Rdefinitions/Rlt.con
+alias Ropp /Coq/Reals/Rdefinitions/Ropp.con
+alias Rinv /Coq/Reals/Rdefinitions/Rinv.con
alias Rplus /Coq/Reals/Rdefinitions/Rplus.con
alias Rminus /Coq/Reals/Rdefinitions/Rminus.con
alias R1 /Coq/Reals/Rdefinitions/R1.con
+alias R0 /Coq/Reals/Rdefinitions/R0.con
alias R /Coq/Reals/Rdefinitions/R.con
+alias Eq /Coq/Init/Logic_Type/eqT.ind#1/1
+//test base1 ok
!x:R.!y:R.(Rle x y) -> (Rge (Rplus y R1) (Rminus x R1))
+
+//test base2 ok
+!x:R.!y:R.(Rlt x y) -> (Rgt (Rplus y R1) (Rminus x R1))
+
+//test base3 (unification fails)
+!x:R.!y:R.(Rge x y) -> (Rlt (Rplus y R1) (Rplus x (Rplus R1 R1)))
+
+//test base4 ok
+!x:R.!y:R.(Rgt x y) -> (Rle (Rminus y R1) (Rplus x R1))
+
+//test base5 ok
+!x:R.!y:R.(Rlt x ( Rplus y R1 ) ) -> (Rge (Rplus y (Rplus R1 R1)) (Rminus x R0))
+
+//test base6 (unification fails)
+!x:R.!y:R.(Eq R x y) -> (Rgt (Rplus y R1) (Rminus x R1))
+
+//test base7 (should fail) ok
+!x:R.!y:R.(Rlt x y) -> (Rlt (Rplus y R1) (Rminus x R1))
+
+