--- a/src/HOL/Real/Hyperreal/Star.ML Thu Dec 21 10:16:07 2000 +0100
+++ b/src/HOL/Real/Hyperreal/Star.ML Thu Dec 21 10:16:33 2000 +0100
@@ -212,6 +212,7 @@
by (res_inst_tac [("z","xa")] eq_Abs_hypreal 1);
by (auto_tac (claset(),simpset() addsimps [starfun,hypreal_mult]));
qed "starfun_mult";
+Addsimps [starfun_mult RS sym];
(*---------------------------------------
addition: ( *f ) + ( *g ) = *(f + g)
@@ -220,6 +221,7 @@
by (res_inst_tac [("z","xa")] eq_Abs_hypreal 1);
by (auto_tac (claset(),simpset() addsimps [starfun,hypreal_add]));
qed "starfun_add";
+Addsimps [starfun_add RS sym];
(*--------------------------------------------
subtraction: ( *f ) + -( *g ) = *(f + -g)
@@ -229,21 +231,25 @@
by (res_inst_tac [("z","x")] eq_Abs_hypreal 1);
by (auto_tac (claset(),simpset() addsimps [starfun, hypreal_minus]));
qed "starfun_minus";
+Addsimps [starfun_minus RS sym];
+(*FIXME: delete*)
Goal "(*f* f) xa + -(*f* g) xa = (*f* (%x. f x + -g x)) xa";
-by (simp_tac (simpset() addsimps [starfun_minus, starfun_add]) 1);
+by (Simp_tac 1);
qed "starfun_add_minus";
+Addsimps [starfun_add_minus RS sym];
Goalw [hypreal_diff_def,real_diff_def]
"(*f* f) xa - (*f* g) xa = (*f* (%x. f x - g x)) xa";
by (rtac starfun_add_minus 1);
qed "starfun_diff";
+Addsimps [starfun_diff RS sym];
(*--------------------------------------
composition: ( *f ) o ( *g ) = *(f o g)
---------------------------------------*)
-Goal "(%x. (*f* f) ((*f* g) x)) = *f* (%x. f (g x))";
+Goal "(%x. (*f* f) ((*f* g) x)) = *f* (%x. f (g x))";
by (rtac ext 1);
by (res_inst_tac [("z","x")] eq_Abs_hypreal 1);
by (auto_tac (claset(),simpset() addsimps [starfun]));
@@ -343,13 +349,12 @@
by (dtac inf_close_mult_HFinite 1);
by (REPEAT(assume_tac 1));
by (auto_tac (claset() addIs [inf_close_sym RSN (2,inf_close_HFinite)],
- simpset() addsimps [starfun_mult]));
+ simpset()));
qed "starfun_mult_HFinite_inf_close";
Goal "[| (*f* f) xa @= l; (*f* g) xa @= m \
\ |] ==> (*f* (%x. f x + g x)) xa @= l + m";
-by (auto_tac (claset() addIs [inf_close_add],
- simpset() addsimps [starfun_add RS sym]));
+by (auto_tac (claset() addIs [inf_close_add], simpset()));
qed "starfun_add_inf_close";
(*----------------------------------------------------
@@ -363,7 +368,7 @@
Goal "*f* abs = abs";
by (rtac (hrabs_is_starext_rabs RS
- (is_starext_starfun_iff RS iffD1) RS sym) 1);
+ (is_starext_starfun_iff RS iffD1) RS sym) 1);
qed "starfun_rabs_hrabs";
Goal "(*f* inverse) x = inverse(x)";
@@ -382,11 +387,13 @@
by (auto_tac (claset(),
simpset() addsimps [starfun, hypreal_inverse]));
qed "starfun_inverse";
+Addsimps [starfun_inverse RS sym];
Goalw [hypreal_divide_def,real_divide_def]
"(*f* f) xa / (*f* g) xa = (*f* (%x. f x / g x)) xa";
-by (simp_tac (simpset() addsimps [starfun_inverse, starfun_mult]) 1);
+by Auto_tac;
qed "starfun_divide";
+Addsimps [starfun_divide RS sym];
Goal "inverse ((*f* f) x) = (*f* (%x. inverse (f x))) x";
by (res_inst_tac [("z","x")] eq_Abs_hypreal 1);
@@ -424,12 +431,13 @@
by its NS extenson ( *f* f). See second NS set extension below.
----------------------------------------------------------------*)
Goalw [starset_def]
- "*s* {x. abs (x + - y) < r} = {x. abs(x + -hypreal_of_real y) < hypreal_of_real r}";
+ "*s* {x. abs (x + - y) < r} = \
+\ {x. abs(x + -hypreal_of_real y) < hypreal_of_real r}";
by (Step_tac 1);
by (ALLGOALS(res_inst_tac [("z","x")] eq_Abs_hypreal));
by (auto_tac (claset() addSIs [exI] addSDs [bspec],
- simpset() addsimps [hypreal_minus, hypreal_of_real_def,hypreal_add,
- hypreal_hrabs,hypreal_less_def]));
+ simpset() addsimps [hypreal_minus, hypreal_of_real_def,hypreal_add,
+ hypreal_hrabs,hypreal_less_def]));
by (Fuf_tac 1);
qed "STAR_rabs_add_minus";