
diff -r 66f3570ba808 -r 03bfbc480107 src/Tools/isac/Knowledge/RootEq.thy
--- a/src/Tools/isac/Knowledge/RootEq.thy	Mon Sep 06 15:53:18 2010 +0200
+++ b/src/Tools/isac/Knowledge/RootEq.thy	Mon Sep 06 16:56:22 2010 +0200
@@ -40,81 +40,81 @@
 axioms 
 
 (* normalize *)
-  makex1_x            "a^^^1  = a"  
-  real_assoc_1        "a+(b+c) = a+b+c"
-  real_assoc_2        "a*(b*c) = a*b*c"
+  makex1_x:            "a^^^1  = a"  
+  real_assoc_1:        "a+(b+c) = a+b+c"
+  real_assoc_2:        "a*(b*c) = a*b*c"
 
   (* simplification of root*)
-  sqrt_square_1       "[|0 <= a|] ==>  (sqrt a)^^^2 = a"
-  sqrt_square_2       "sqrt (a ^^^ 2) = a"
-  sqrt_times_root_1   "sqrt a * sqrt b = sqrt(a*b)"
-  sqrt_times_root_2   "a * sqrt b * sqrt c = a * sqrt(b*c)"
+  sqrt_square_1:       "[|0 <= a|] ==>  (sqrt a)^^^2 = a"
+  sqrt_square_2:       "sqrt (a ^^^ 2) = a"
+  sqrt_times_root_1:   "sqrt a * sqrt b = sqrt(a*b)"
+  sqrt_times_root_2:   "a * sqrt b * sqrt c = a * sqrt(b*c)"
 
   (* isolate one root on the LEFT or RIGHT hand side of the equation *)
-  sqrt_isolate_l_add1 "[|bdv occurs_in c|] ==> 
+  sqrt_isolate_l_add1: "[|bdv occurs_in c|] ==> 
    (a + b*sqrt(c) = d) = (b * sqrt(c) = d+ (-1) * a)"
-  sqrt_isolate_l_add2 "[|bdv occurs_in c|] ==>
+  sqrt_isolate_l_add2: "[|bdv occurs_in c|] ==>
    (a + sqrt(c) = d) = ((sqrt(c) = d+ (-1) * a))"
-  sqrt_isolate_l_add3 "[|bdv occurs_in c|] ==>
+  sqrt_isolate_l_add3: "[|bdv occurs_in c|] ==>
    (a + b*(e/sqrt(c)) = d) = (b * (e/sqrt(c)) = d + (-1) * a)"
-  sqrt_isolate_l_add4 "[|bdv occurs_in c|] ==>
+  sqrt_isolate_l_add4: "[|bdv occurs_in c|] ==>
    (a + b/(f*sqrt(c)) = d) = (b / (f*sqrt(c)) = d + (-1) * a)"
-  sqrt_isolate_l_add5 "[|bdv occurs_in c|] ==>
+  sqrt_isolate_l_add5: "[|bdv occurs_in c|] ==>
    (a + b*(e/(f*sqrt(c))) = d) = (b * (e/(f*sqrt(c))) = d+ (-1) * a)"
-  sqrt_isolate_l_add6 "[|bdv occurs_in c|] ==>
+  sqrt_isolate_l_add6: "[|bdv occurs_in c|] ==>
    (a + b/sqrt(c) = d) = (b / sqrt(c) = d+ (-1) * a)"
-  sqrt_isolate_r_add1 "[|bdv occurs_in f|] ==>
+  sqrt_isolate_r_add1: "[|bdv occurs_in f|] ==>
    (a = d + e*sqrt(f)) = (a + (-1) * d = e*sqrt(f))"
-  sqrt_isolate_r_add2 "[|bdv occurs_in f|] ==>
+  sqrt_isolate_r_add2: "[|bdv occurs_in f|] ==>
    (a = d + sqrt(f)) = (a + (-1) * d = sqrt(f))"
  (* small hack: thm 3,5,6 are not needed if rootnormalize is well done*)
-  sqrt_isolate_r_add3 "[|bdv occurs_in f|] ==>
+  sqrt_isolate_r_add3: "[|bdv occurs_in f|] ==>
    (a = d + e*(g/sqrt(f))) = (a + (-1) * d = e*(g/sqrt(f)))"
-  sqrt_isolate_r_add4 "[|bdv occurs_in f|] ==>
+  sqrt_isolate_r_add4: "[|bdv occurs_in f|] ==>
    (a = d + g/sqrt(f)) = (a + (-1) * d = g/sqrt(f))"
-  sqrt_isolate_r_add5 "[|bdv occurs_in f|] ==>
+  sqrt_isolate_r_add5: "[|bdv occurs_in f|] ==>
    (a = d + e*(g/(h*sqrt(f)))) = (a + (-1) * d = e*(g/(h*sqrt(f))))"
-  sqrt_isolate_r_add6 "[|bdv occurs_in f|] ==>
+  sqrt_isolate_r_add6: "[|bdv occurs_in f|] ==>
    (a = d + g/(h*sqrt(f))) = (a + (-1) * d = g/(h*sqrt(f)))"
  
   (* eliminate isolates sqrt *)
-  sqrt_square_equation_both_1 "[|bdv occurs_in b; bdv occurs_in d|] ==> 
+  sqrt_square_equation_both_1: "[|bdv occurs_in b; bdv occurs_in d|] ==> 
    ( (sqrt a + sqrt b         = sqrt c + sqrt d) = 
      (a+2*sqrt(a)*sqrt(b)+b  = c+2*sqrt(c)*sqrt(d)+d))"
-  sqrt_square_equation_both_2 "[|bdv occurs_in b; bdv occurs_in d|] ==> 
+  sqrt_square_equation_both_2: "[|bdv occurs_in b; bdv occurs_in d|] ==> 
    ( (sqrt a - sqrt b           = sqrt c + sqrt d) = 
      (a - 2*sqrt(a)*sqrt(b)+b  = c+2*sqrt(c)*sqrt(d)+d))"
-  sqrt_square_equation_both_3 "[|bdv occurs_in b; bdv occurs_in d|] ==> 
+  sqrt_square_equation_both_3: "[|bdv occurs_in b; bdv occurs_in d|] ==> 
    ( (sqrt a + sqrt b           = sqrt c - sqrt d) = 
      (a + 2*sqrt(a)*sqrt(b)+b  = c - 2*sqrt(c)*sqrt(d)+d))"
-  sqrt_square_equation_both_4 "[|bdv occurs_in b; bdv occurs_in d|] ==> 
+  sqrt_square_equation_both_4: "[|bdv occurs_in b; bdv occurs_in d|] ==> 
    ( (sqrt a - sqrt b           = sqrt c - sqrt d) = 
      (a - 2*sqrt(a)*sqrt(b)+b  = c - 2*sqrt(c)*sqrt(d)+d))"
-  sqrt_square_equation_left_1 "[|bdv occurs_in a; 0 <= a; 0 <= b|] ==>
+  sqrt_square_equation_left_1: "[|bdv occurs_in a; 0 <= a; 0 <= b|] ==>
    ( (sqrt (a) = b) = (a = (b^^^2)))"
-  sqrt_square_equation_left_2 "[|bdv occurs_in a; 0 <= a; 0 <= b*c|] ==> 
+  sqrt_square_equation_left_2: "[|bdv occurs_in a; 0 <= a; 0 <= b*c|] ==> 
    ( (c*sqrt(a) = b) = (c^^^2*a = b^^^2))"
-  sqrt_square_equation_left_3 "[|bdv occurs_in a; 0 <= a; 0 <= b*c|] ==> 
+  sqrt_square_equation_left_3: "[|bdv occurs_in a; 0 <= a; 0 <= b*c|] ==> 
    ( c/sqrt(a) = b) = (c^^^2 / a = b^^^2)"
   (* small hack: thm 4-6 are not needed if rootnormalize is well done*)
-  sqrt_square_equation_left_4 "[|bdv occurs_in a; 0 <= a; 0 <= b*c*d|] ==> 
+  sqrt_square_equation_left_4: "[|bdv occurs_in a; 0 <= a; 0 <= b*c*d|] ==> 
    ( (c*(d/sqrt (a)) = b) = (c^^^2*(d^^^2/a) = b^^^2))"
-  sqrt_square_equation_left_5 "[|bdv occurs_in a; 0 <= a; 0 <= b*c*d|] ==> 
+  sqrt_square_equation_left_5: "[|bdv occurs_in a; 0 <= a; 0 <= b*c*d|] ==> 
    ( c/(d*sqrt(a)) = b) = (c^^^2 / (d^^^2*a) = b^^^2)"
-  sqrt_square_equation_left_6 "[|bdv occurs_in a; 0 <= a; 0 <= b*c*d*e|] ==> 
+  sqrt_square_equation_left_6: "[|bdv occurs_in a; 0 <= a; 0 <= b*c*d*e|] ==> 
    ( (c*(d/(e*sqrt (a))) = b) = (c^^^2*(d^^^2/(e^^^2*a)) = b^^^2))"
-  sqrt_square_equation_right_1  "[|bdv occurs_in b; 0 <= a; 0 <= b|] ==> 
+  sqrt_square_equation_right_1:  "[|bdv occurs_in b; 0 <= a; 0 <= b|] ==> 
    ( (a = sqrt (b)) = (a^^^2 = b))"
-  sqrt_square_equation_right_2 "[|bdv occurs_in b; 0 <= a*c; 0 <= b|] ==> 
+  sqrt_square_equation_right_2: "[|bdv occurs_in b; 0 <= a*c; 0 <= b|] ==> 
    ( (a = c*sqrt (b)) = ((a^^^2) = c^^^2*b))"
-  sqrt_square_equation_right_3 "[|bdv occurs_in b; 0 <= a*c; 0 <= b|] ==> 
+  sqrt_square_equation_right_3: "[|bdv occurs_in b; 0 <= a*c; 0 <= b|] ==> 
    ( (a = c/sqrt (b)) = (a^^^2 = c^^^2/b))"
  (* small hack: thm 4-6 are not needed if rootnormalize is well done*)
-  sqrt_square_equation_right_4 "[|bdv occurs_in b; 0 <= a*c*d; 0 <= b|] ==> 
+  sqrt_square_equation_right_4: "[|bdv occurs_in b; 0 <= a*c*d; 0 <= b|] ==> 
    ( (a = c*(d/sqrt (b))) = ((a^^^2) = c^^^2*(d^^^2/b)))"
-  sqrt_square_equation_right_5 "[|bdv occurs_in b; 0 <= a*c*d; 0 <= b|] ==> 
+  sqrt_square_equation_right_5: "[|bdv occurs_in b; 0 <= a*c*d; 0 <= b|] ==> 
    ( (a = c/(d*sqrt (b))) = (a^^^2 = c^^^2/(d^^^2*b)))"
-  sqrt_square_equation_right_6 "[|bdv occurs_in b; 0 <= a*c*d*e; 0 <= b|] ==> 
+  sqrt_square_equation_right_6: "[|bdv occurs_in b; 0 <= a*c*d*e; 0 <= b|] ==> 
    ( (a = c*(d/(e*sqrt (b)))) = ((a^^^2) = c^^^2*(d^^^2/(e^^^2*b))))"
 
 ML {*




