src/HOLCF/Lift1.ML

     Copyright   1993  Technische Universitaet Muenchen
 *)
 
 open Lift1;
 
-val Exh_Lift = prove_goalw Lift1.thy [UU_lift_def,Iup_def ]
+qed_goalw "Exh_Lift" Lift1.thy [UU_lift_def,Iup_def ]
 	"z = UU_lift | (? x. z = Iup(x))"
  (fn prems =>
 	[
 	(rtac (Rep_Lift_inverse RS subst) 1),
 	(res_inst_tac [("s","Rep_Lift(z)")] sumE 1),

 	(rtac exI 1),
 	(res_inst_tac [("f","Abs_Lift")] arg_cong 1),
 	(atac 1)
 	]);
 
-val inj_Abs_Lift = prove_goal Lift1.thy "inj(Abs_Lift)"
+qed_goal "inj_Abs_Lift" Lift1.thy "inj(Abs_Lift)"
  (fn prems =>
 	[
 	(rtac inj_inverseI 1),
 	(rtac Abs_Lift_inverse 1)
 	]);
 
-val inj_Rep_Lift = prove_goal Lift1.thy "inj(Rep_Lift)"
+qed_goal "inj_Rep_Lift" Lift1.thy "inj(Rep_Lift)"
  (fn prems =>
 	[
 	(rtac inj_inverseI 1),
 	(rtac Rep_Lift_inverse 1)
 	]);
 
-val inject_Iup = prove_goalw Lift1.thy [Iup_def] "Iup(x)=Iup(y) ==> x=y"
+qed_goalw "inject_Iup" Lift1.thy [Iup_def] "Iup(x)=Iup(y) ==> x=y"
  (fn prems =>
 	[
 	(cut_facts_tac prems 1),
 	(rtac (inj_Inr RS injD) 1),
 	(rtac (inj_Abs_Lift RS injD) 1),
 	(atac 1)
 	]);
 
-val defined_Iup=prove_goalw Lift1.thy [Iup_def,UU_lift_def] "~ Iup(x)=UU_lift"
+qed_goalw "defined_Iup" Lift1.thy [Iup_def,UU_lift_def] "~ Iup(x)=UU_lift"
  (fn prems =>
 	[
 	(rtac notI 1),
 	(rtac notE 1),
 	(rtac Inl_not_Inr 1),
 	(rtac sym 1),
 	(etac (inj_Abs_Lift RS  injD) 1)
 	]);
 
 
-val liftE = prove_goal  Lift1.thy
+qed_goal "liftE"  Lift1.thy
 	"[| p=UU_lift ==> Q; !!x. p=Iup(x)==>Q|] ==>Q"
  (fn prems =>
 	[
 	(rtac (Exh_Lift RS disjE) 1),
 	(eresolve_tac prems 1),
 	(etac exE 1),
 	(eresolve_tac prems 1)
 	]);
 
-val Ilift1 = prove_goalw  Lift1.thy [Ilift_def,UU_lift_def]
+qed_goalw "Ilift1"  Lift1.thy [Ilift_def,UU_lift_def]
 	"Ilift(f)(UU_lift)=UU"
  (fn prems =>
 	[
 	(rtac (Abs_Lift_inverse RS ssubst) 1),
 	(rtac (sum_case_Inl RS ssubst) 1),
 	(rtac refl 1)
 	]);
 
-val Ilift2 = prove_goalw  Lift1.thy [Ilift_def,Iup_def]
+qed_goalw "Ilift2"  Lift1.thy [Ilift_def,Iup_def]
 	"Ilift(f)(Iup(x))=f[x]"
  (fn prems =>
 	[
 	(rtac (Abs_Lift_inverse RS ssubst) 1),
 	(rtac (sum_case_Inr RS ssubst) 1),
 	(rtac refl 1)
 	]);
 
 val Lift_ss = Cfun_ss addsimps [Ilift1,Ilift2];
 
-val less_lift1a = prove_goalw  Lift1.thy [less_lift_def,UU_lift_def]
+qed_goalw "less_lift1a"  Lift1.thy [less_lift_def,UU_lift_def]
 	"less_lift(UU_lift)(z)"
  (fn prems =>
 	[
 	(rtac (Abs_Lift_inverse RS ssubst) 1),
 	(rtac (sum_case_Inl RS ssubst) 1),
 	(rtac TrueI 1)
 	]);
 
-val less_lift1b = prove_goalw  Lift1.thy [Iup_def,less_lift_def,UU_lift_def]
+qed_goalw "less_lift1b"  Lift1.thy [Iup_def,less_lift_def,UU_lift_def]
 	"~less_lift(Iup(x),UU_lift)"
  (fn prems =>
 	[
 	(rtac notI 1),
 	(rtac iffD1 1),

 	(rtac (sum_case_Inr RS ssubst) 1),
 	(rtac (sum_case_Inl RS ssubst) 1),
 	(rtac refl 1)
 	]);
 
-val less_lift1c = prove_goalw  Lift1.thy [Iup_def,less_lift_def,UU_lift_def]
+qed_goalw "less_lift1c"  Lift1.thy [Iup_def,less_lift_def,UU_lift_def]
 	"less_lift(Iup(x),Iup(y))=(x<<y)"
  (fn prems =>
 	[
 	(rtac (Abs_Lift_inverse RS ssubst) 1),
 	(rtac (Abs_Lift_inverse RS ssubst) 1),

 	(rtac (sum_case_Inr RS ssubst) 1),
 	(rtac refl 1)
 	]);
 
 
-val refl_less_lift = prove_goal  Lift1.thy "less_lift(p,p)"
+qed_goal "refl_less_lift"  Lift1.thy "less_lift(p,p)"
  (fn prems =>
 	[
 	(res_inst_tac [("p","p")] liftE 1),
 	(hyp_subst_tac 1),
 	(rtac less_lift1a 1),
 	(hyp_subst_tac 1),
 	(rtac (less_lift1c RS iffD2) 1),
 	(rtac refl_less 1)
 	]);
 
-val antisym_less_lift = prove_goal  Lift1.thy 
+qed_goal "antisym_less_lift"  Lift1.thy 
 	"[|less_lift(p1,p2);less_lift(p2,p1)|] ==> p1=p2"
  (fn prems =>
 	[
 	(cut_facts_tac prems 1),
 	(res_inst_tac [("p","p1")] liftE 1),

 	(rtac antisym_less 1),
 	(etac (less_lift1c RS iffD1) 1),
 	(etac (less_lift1c RS iffD1) 1)
 	]);
 
-val trans_less_lift = prove_goal  Lift1.thy 
+qed_goal "trans_less_lift"  Lift1.thy 
 	"[|less_lift(p1,p2);less_lift(p2,p3)|] ==> less_lift(p1,p3)"
  (fn prems =>
 	[
 	(cut_facts_tac prems 1),
 	(res_inst_tac [("p","p1")] liftE 1),