An old bug in 'eqT' hipotesys solved

[helm.git] / helm / gTopLevel / esempi / fourier.cic

diff --git a/helm/gTopLevel/esempi/fourier.cic b/helm/gTopLevel/esempi/fourier.cic
index a76b4586a2076712830eccd035a83c702f29e0ca..dc883e4e4888fd11463339122b528af7320bd3d7 100644 (file)
--- a/helm/gTopLevel/esempi/fourier.cic
+++ b/helm/gTopLevel/esempi/fourier.cic
@@ -6,10 +6,13 @@ 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 Rmult    /Coq/Reals/Rdefinitions/Rmult.con
 alias R1        /Coq/Reals/Rdefinitions/R1.con
 alias R0        /Coq/Reals/Rdefinitions/R0.con
 alias R        /Coq/Reals/Rdefinitions/R.con
 alias eqT      /Coq/Init/Logic_Type/eqT.ind#1/1
+alias not      /Coq/Init/Logic/not.con
+
 
 //test base1 ok
 !x:R.!y:R.(Rle x y) -> (Rge (Rplus y R1) (Rminus x R1))
@@ -20,13 +23,28 @@ alias eqT   /Coq/Init/Logic_Type/eqT.ind#1/1
 //test base3 ok
 !x:R.!y:R.(Rge x y) -> (Rlt (Rplus y R1) (Rplus x (Rplus R1 R1)))
 
+/Coq/fourier/Fourier_util/Rfourier_not_ge_lt.con
+
+/Coq/Init/Logic/False.ind#1/1
+
+(Rle (Rplus (Rmult (Rmult R1 (Rinv R1)) (Rplus x (Rplus R1 R1))) (Rmult (Rmult R1 (Rinv R1)) y)) (Rplus (Rmult (Rmult R1 (Rinv R1)) (Rplus y R1)) (Rmult (Rmult R1 (Rinv R1)) x)))
+
+/Coq/fourier/Fourier_util/Rnot_le_le.con
+
+t1=(Rplus (Rmult (Rmult R1 (Rinv R1)) (Rplus x (Rplus R1 R1))) (Rmult (Rmult R1 (Rinv R1)) y))
+t2=(Rplus (Rmult (Rmult R1 (Rinv R1)) (Rplus y R1)) (Rmult (Rmult R1 (Rinv R1)) x))
+tc=(Rmult (Ropp R1) (Rinv R1))
+
+rewrite=(eqT R (Rminus (Rplus (Rmult (Rmult R1 (Rinv R1)) (Rplus y R1)) (Rmult (Rmult R1 (Rinv R1)) x))
+ (Rplus (Rmult (Rmult R1 (Rinv R1)) (Rplus x (Rplus R1 R1))) (Rmult (Rmult R1 (Rinv R1)) y))) (Rmult (Ropp R1) (Rinv 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 (fourier fails)
+//test base6 ok
 !x:R.!y:R.(eqT R x y) -> (Rgt (Rplus y R1) (Rminus x R1))
 
 //test base7 (should fail) ok