Merge of the V7_3_new_exportation branch.

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

diff --git a/helm/gTopLevel/esempi/fourier/fourier.cic b/helm/gTopLevel/esempi/fourier/fourier.cic
new file mode 100644 (file)
index 0000000..23062f3
--- /dev/null
+++ b/helm/gTopLevel/esempi/fourier/fourier.cic
@@ -0,0 +1,137 @@
+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 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
+alias or /Coq/Init/Logic/or.ind#1/1
+
+!x:R.
+(Rlt (Rmult(Ropp x)R1)
+R0)
+->(Rlt R0 x)
+
+// test 3x4 -> 35''
+!x:R.!y:R.!z:R.
+(Rge
+(Rplus
+ (Rmult (Ropp (Rplus R1 R1)) x) (Rplus 
+   (Rmult (Rplus R1 (Rplus R1 (Rplus R1 (Rplus R1 R1)))) y) (Rplus 
+     (Rmult (Rplus R1 (Rplus R1 R1)) z) R1)
+)) R0)
+->  
+(Rge
+(Rplus
+ (Rmult (Ropp (Rplus R1 (Rplus R1 R1))) x) (Rplus 
+   (Rmult (Ropp (Rplus R1 (Rplus R1 (Rplus R1 (Rplus R1 (Rplus R1 R1)))))) y) (Rplus 
+      R1 (Rplus R1 R1))
+)) R0)
+->  
+(Rgt
+(Rplus
+  x (Rplus 
+   (Rmult (Rplus R1 R1) y) (Ropp z) )
+) R0)
+-> 
+(Rgt
+(Rplus
+ (Rmult (Rplus R1 (Rplus R1 R1)) x) (Rplus 
+   z (Ropp R1))
+) R0)
+
+-> (Rlt z R1)
+
+// test 6x6 -> 
+
+!x:R.!y:R.!z:R.!t:R.!u:R.!v:R.
+(Rgt
+(Rplus (Ropp x) (Rplus y (Rplus z (Rplus t (Rplus u (Rplus v (Rplus R1 R1)))))))
+  R0)
+->
+(Rgt
+(Rplus x (Rplus (Ropp y) (Rplus (Ropp z) (Rplus (Ropp t) (Rplus (Ropp u) (Rplus R1 R1))))))
+  R0)
+->
+(Rgt
+(Rplus y (Rplus (Ropp z) (Rplus t (Rplus u (Rplus R1 R1)))))
+  R0)
+->
+(Rgt
+(Rplus y (Rplus z (Rplus (Ropp t) (Rplus (Ropp (Rmult (Rplus R1 R1)v)) (Rplus R1 R1)))))
+  R0)
+->
+(Rgt
+(Rplus y (Rplus z (Rplus t (Rplus (Ropp u) (Rplus R1 R1)))))
+  R0)
+->
+(Rlt
+(Rplus (Rmult (Rplus R1 R1) x) (Rplus v y))
+  R0)
+-> (Rlt (Rmult (Rplus R1 R1) x) R0)
+
+
+
+
+
+
+//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 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
+
+intros
+
+/Coq/Init/Logic/False.ind#1/1
+
+(not (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))
+
+(t1-t2)=(Rminus 
+(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)))
+
+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)))
+
+change=(not (or 
+(Rlt R0 (Rmult (Ropp R1) (Rinv R1))) 
+(eqT R R0 (Rmult (Ropp R1) (Rinv R1))) 
+))
+
+tac2
+/Coq/fourier/Fourier_util/Rnot_lt0.con
+
+//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 ok
+!x:R.!y:R.(eqT 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))
+
+