src/HOLCF/Lift3.ML
author clasohm
Tue, 24 Oct 1995 14:45:35 +0100
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(*  Title: 	HOLCF/lift3.ML
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    ID:         $Id$
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    Author: 	Franz Regensburger
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    Copyright   1993 Technische Universitaet Muenchen
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Lemmas for lift3.thy
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*)
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open Lift3;
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(* -------------------------------------------------------------------------*)
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(* some lemmas restated for class pcpo                                      *)
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(* ------------------------------------------------------------------------ *)
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qed_goal "less_lift3b" Lift3.thy "~ Iup(x) << UU"
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 (fn prems =>
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	[
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	(rtac (inst_lift_pcpo RS ssubst) 1),
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	(rtac less_lift2b 1)
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	]);
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qed_goal "defined_Iup2" Lift3.thy "Iup(x) ~= UU"
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 (fn prems =>
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	[
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	(rtac (inst_lift_pcpo RS ssubst) 1),
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	(rtac defined_Iup 1)
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	]);
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(* ------------------------------------------------------------------------ *)
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(* continuity for Iup                                                       *)
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(* ------------------------------------------------------------------------ *)
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qed_goal "contlub_Iup" Lift3.thy "contlub(Iup)"
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 (fn prems =>
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	[
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	(rtac contlubI 1),
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	(strip_tac 1),
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	(rtac trans 1),
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	(rtac (thelub_lift1a RS sym) 2),
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	(fast_tac HOL_cs 3),
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	(etac (monofun_Iup RS ch2ch_monofun) 2),
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	(res_inst_tac [("f","Iup")] arg_cong  1),
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	(rtac lub_equal 1),
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	(atac 1),
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	(rtac (monofun_Ilift2 RS ch2ch_monofun) 1),
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	(etac (monofun_Iup RS ch2ch_monofun) 1),
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        (asm_simp_tac Lift0_ss 1)
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	]);
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qed_goal "cont_Iup" Lift3.thy "cont(Iup)"
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 (fn prems =>
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	[
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	(rtac monocontlub2cont 1),
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	(rtac monofun_Iup 1),
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	(rtac contlub_Iup 1)
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	]);
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(* ------------------------------------------------------------------------ *)
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(* continuity for Ilift                                                     *)
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(* ------------------------------------------------------------------------ *)
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qed_goal "contlub_Ilift1" Lift3.thy "contlub(Ilift)"
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 (fn prems =>
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	[
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	(rtac contlubI 1),
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	(strip_tac 1),
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	(rtac trans 1),
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	(rtac (thelub_fun RS sym) 2),
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	(etac (monofun_Ilift1 RS ch2ch_monofun) 2),
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	(rtac ext 1),
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	(res_inst_tac [("p","x")] liftE 1),
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        (asm_simp_tac Lift0_ss 1),
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	(rtac (lub_const RS thelubI RS sym) 1),
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        (asm_simp_tac Lift0_ss 1),
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	(etac contlub_cfun_fun 1)
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	]);
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qed_goal "contlub_Ilift2" Lift3.thy "contlub(Ilift(f))"
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 (fn prems =>
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	[
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	(rtac contlubI 1),
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	(strip_tac 1),
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	(rtac disjE 1),
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	(rtac (thelub_lift1a RS ssubst) 2),
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	(atac 2),
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	(atac 2),
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        (asm_simp_tac Lift0_ss 2),
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	(rtac (thelub_lift1b RS ssubst) 3),
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	(atac 3),
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	(atac 3),
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	(fast_tac HOL_cs 1),
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        (asm_simp_tac Lift0_ss 2),
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	(rtac (chain_UU_I_inverse RS sym) 2),
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	(rtac allI 2),
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	(res_inst_tac [("p","Y(i)")] liftE 2),
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        (asm_simp_tac Lift0_ss 2),
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	(rtac notE 2),
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	(dtac spec 2),
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	(etac spec 2),
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	(atac 2),
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	(rtac (contlub_cfun_arg RS ssubst) 1),
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	(etac (monofun_Ilift2 RS ch2ch_monofun) 1),
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	(rtac lub_equal2 1),
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	(rtac (monofun_fapp2 RS ch2ch_monofun) 2),
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	(etac (monofun_Ilift2 RS ch2ch_monofun) 2),
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	(etac (monofun_Ilift2 RS ch2ch_monofun) 2),
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	(rtac (chain_mono2 RS exE) 1),
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	(atac 2),
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	(etac exE 1),
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	(etac exE 1),
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	(rtac exI 1),
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	(res_inst_tac [("s","Iup(x)"),("t","Y(i)")] ssubst 1),
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	(atac 1),
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	(rtac defined_Iup2 1),
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	(rtac exI 1),
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	(strip_tac 1),
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	(res_inst_tac [("p","Y(i)")] liftE 1),
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        (asm_simp_tac Lift0_ss 2),
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	(res_inst_tac [("P","Y(i) = UU")] notE 1),
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	(fast_tac HOL_cs 1),
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	(rtac (inst_lift_pcpo RS ssubst) 1),
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	(atac 1)
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	]);
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qed_goal "cont_Ilift1" Lift3.thy "cont(Ilift)"
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 (fn prems =>
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	[
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	(rtac monocontlub2cont 1),
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	(rtac monofun_Ilift1 1),
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	(rtac contlub_Ilift1 1)
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	]);
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qed_goal "cont_Ilift2" Lift3.thy "cont(Ilift(f))"
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 (fn prems =>
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	[
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	(rtac monocontlub2cont 1),
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	(rtac monofun_Ilift2 1),
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	(rtac contlub_Ilift2 1)
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	]);
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(* ------------------------------------------------------------------------ *)
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(* continuous versions of lemmas for ('a)u                                  *)
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(* ------------------------------------------------------------------------ *)
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qed_goalw "Exh_Lift1" Lift3.thy [up_def] "z = UU | (? x. z = up`x)"
243
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 (fn prems =>
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	[
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        (simp_tac (Lift0_ss addsimps [cont_Iup]) 1),
243
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	(rtac (inst_lift_pcpo RS ssubst) 1),
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	(rtac Exh_Lift 1)
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	]);
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qed_goalw "inject_up" Lift3.thy [up_def] "up`x=up`y ==> x=y"
243
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 (fn prems =>
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	[
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	(cut_facts_tac prems 1),
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	(rtac inject_Iup 1),
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	(etac box_equals 1),
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        (simp_tac (Lift0_ss addsimps [cont_Iup]) 1),
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        (simp_tac (Lift0_ss addsimps [cont_Iup]) 1)
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 	]);
243
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qed_goalw "defined_up" Lift3.thy [up_def] " up`x ~= UU"
243
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 (fn prems =>
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	[
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        (simp_tac (Lift0_ss addsimps [cont_Iup]) 1),
243
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	(rtac defined_Iup2 1)
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	]);
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892
d0dc8d057929 added qed, qed_goal[w]
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qed_goalw "liftE1" Lift3.thy [up_def] 
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	"[| p=UU ==> Q; !!x. p=up`x==>Q|] ==>Q"
243
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 (fn prems =>
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	[
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	(rtac liftE 1),
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	(resolve_tac prems 1),
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	(etac (inst_lift_pcpo RS ssubst) 1),
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	(resolve_tac (tl prems) 1),
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        (asm_simp_tac (Lift0_ss addsimps [cont_Iup]) 1)
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	]);
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qed_goalw "lift1" Lift3.thy [up_def,lift_def] "lift`f`UU=UU"
243
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 (fn prems =>
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	[
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	(rtac (inst_lift_pcpo RS ssubst) 1),
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	(rtac (beta_cfun RS ssubst) 1),
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	(REPEAT (resolve_tac (cont_lemmas @ [cont_Iup,cont_Ilift1,
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		cont_Ilift2,cont2cont_CF1L]) 1)),
243
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	(rtac (beta_cfun RS ssubst) 1),
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	(REPEAT (resolve_tac (cont_lemmas @ [cont_Iup,cont_Ilift1,
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		cont_Ilift2,cont2cont_CF1L]) 1)),
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	(simp_tac (Lift0_ss addsimps [cont_Iup,cont_Ilift1,cont_Ilift2]) 1)
243
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	]);
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qed_goalw "lift2" Lift3.thy [up_def,lift_def] "lift`f`(up`x)=f`x"
243
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 (fn prems =>
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	[
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	(rtac (beta_cfun RS ssubst) 1),
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	(rtac cont_Iup 1),
243
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	(rtac (beta_cfun RS ssubst) 1),
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	(REPEAT (resolve_tac (cont_lemmas @ [cont_Iup,cont_Ilift1,
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		cont_Ilift2,cont2cont_CF1L]) 1)),
243
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	(rtac (beta_cfun RS ssubst) 1),
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	(rtac cont_Ilift2 1),
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	(simp_tac (Lift0_ss addsimps [cont_Iup,cont_Ilift1,cont_Ilift2]) 1)
243
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	]);
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qed_goalw "less_lift4b" Lift3.thy [up_def,lift_def] "~ up`x << UU"
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 (fn prems =>
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	[
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        (simp_tac (Lift0_ss addsimps [cont_Iup]) 1),
243
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	(rtac less_lift3b 1)
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	]);
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qed_goalw "less_lift4c" Lift3.thy [up_def,lift_def]
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	 "(up`x << up`y) = (x<<y)"
243
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 (fn prems =>
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	[
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        (simp_tac (Lift0_ss addsimps [cont_Iup]) 1),
243
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	(rtac less_lift2c 1)
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	]);
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892
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qed_goalw "thelub_lift2a" Lift3.thy [up_def,lift_def] 
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"[| is_chain(Y); ? i x. Y(i) = up`x |] ==>\
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\      lub(range(Y)) = up`(lub(range(%i. lift`(LAM x. x)`(Y i))))"
243
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 (fn prems =>
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	[
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	(cut_facts_tac prems 1),
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	(rtac (beta_cfun RS ssubst) 1),
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   233
	(REPEAT (resolve_tac (cont_lemmas @ [cont_Iup,cont_Ilift1,
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		cont_Ilift2,cont2cont_CF1L]) 1)),
243
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	(rtac (beta_cfun RS ssubst) 1),
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parents: 892
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   236
	(REPEAT (resolve_tac (cont_lemmas @ [cont_Iup,cont_Ilift1,
74be52691d62 The curried version of HOLCF is now just called HOLCF. The old
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		cont_Ilift2,cont2cont_CF1L]) 1)),
243
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	(rtac (beta_cfun RS ext RS ssubst) 1),
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   240
	(REPEAT (resolve_tac (cont_lemmas @ [cont_Iup,cont_Ilift1,
74be52691d62 The curried version of HOLCF is now just called HOLCF. The old
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		cont_Ilift2,cont2cont_CF1L]) 1)),
243
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	(rtac thelub_lift1a 1),
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	(atac 1),
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	(etac exE 1),
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	(etac exE 1),
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   246
	(rtac exI 1),
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   247
	(rtac exI 1),
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	(etac box_equals 1),
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	(rtac refl 1),
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	(simp_tac (Lift0_ss addsimps [cont_Iup]) 1)
243
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	]);
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892
d0dc8d057929 added qed, qed_goal[w]
clasohm
parents: 243
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   255
qed_goalw "thelub_lift2b" Lift3.thy [up_def,lift_def] 
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   256
"[| is_chain(Y); ! i x. Y(i) ~= up`x |] ==> lub(range(Y)) = UU"
243
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 (fn prems =>
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	[
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	(cut_facts_tac prems 1),
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	(rtac (inst_lift_pcpo RS ssubst) 1),
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   261
	(rtac thelub_lift1b 1),
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	(atac 1),
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   263
	(strip_tac 1),
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   264
	(dtac spec 1),
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   265
	(dtac spec 1),
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   266
	(rtac swap 1),
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   267
	(atac 1),
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   268
	(dtac notnotD 1),
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	(etac box_equals 1),
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	(rtac refl 1),
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        (simp_tac (Lift0_ss addsimps [cont_Iup]) 1)
243
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	]);
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   273
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qed_goal "lift_lemma2" Lift3.thy  " (? x.z = up`x) = (z~=UU)"
243
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 (fn prems =>
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	[
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	(rtac iffI 1),
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   279
	(etac exE 1),
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   280
	(hyp_subst_tac 1),
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   281
	(rtac defined_up 1),
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   282
	(res_inst_tac [("p","z")] liftE1 1),
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   283
	(etac notE 1),
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	(atac 1),
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	(etac exI 1)
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	]);
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   287
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892
d0dc8d057929 added qed, qed_goal[w]
clasohm
parents: 243
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qed_goal "thelub_lift2a_rev" Lift3.thy  
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"[| is_chain(Y); lub(range(Y)) = up`x |] ==> ? i x. Y(i) = up`x"
243
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 (fn prems =>
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	[
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	(cut_facts_tac prems 1),
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	(rtac exE 1),
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	(rtac chain_UU_I_inverse2 1),
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	(rtac (lift_lemma2 RS iffD1) 1),
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   297
	(etac exI 1),
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   298
	(rtac exI 1),
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	(rtac (lift_lemma2 RS iffD2) 1),
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	(atac 1)
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	]);
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892
d0dc8d057929 added qed, qed_goal[w]
clasohm
parents: 243
diff changeset
   303
qed_goal "thelub_lift2b_rev" Lift3.thy  
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74be52691d62 The curried version of HOLCF is now just called HOLCF. The old
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parents: 892
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   304
"[| is_chain(Y); lub(range(Y)) = UU |] ==> ! i x.  Y(i) ~= up`x"
243
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 (fn prems =>
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	[
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	(cut_facts_tac prems 1),
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	(rtac allI 1),
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	(rtac (notex2all RS iffD1) 1),
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	(rtac contrapos 1),
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	(etac (lift_lemma2 RS iffD1) 2),
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	(rtac notnotI 1),
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	(rtac (chain_UU_I RS spec) 1),
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   314
	(atac 1),
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	(atac 1)
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	]);
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   317
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892
d0dc8d057929 added qed, qed_goal[w]
clasohm
parents: 243
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qed_goal "thelub_lift3" Lift3.thy  
243
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"is_chain(Y) ==> lub(range(Y)) = UU |\
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regensbu
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\                lub(range(Y)) = up`(lub(range(%i. lift`(LAM x.x)`(Y i))))"
243
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 (fn prems =>
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	[
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	(cut_facts_tac prems 1),
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	(rtac disjE 1),
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   326
	(rtac disjI1 2),
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   327
	(rtac thelub_lift2b 2),
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   328
	(atac 2),
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   329
	(atac 2),
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   330
	(rtac disjI2 2),
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   331
	(rtac thelub_lift2a 2),
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   332
	(atac 2),
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   333
	(atac 2),
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	(fast_tac HOL_cs 1)
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	]);
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1168
74be52691d62 The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents: 892
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   337
qed_goal "lift3" Lift3.thy "lift`up`x=x"
243
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   338
 (fn prems =>
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	[
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	(res_inst_tac [("p","x")] liftE1 1),
1277
caef3601c0b2 corrected some errors that occurred after introduction of local simpsets
regensbu
parents: 1274
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   341
	(asm_simp_tac ((simpset_of "Cfun3") addsimps [lift1,lift2]) 1),
caef3601c0b2 corrected some errors that occurred after introduction of local simpsets
regensbu
parents: 1274
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	(asm_simp_tac ((simpset_of "Cfun3") addsimps [lift1,lift2]) 1)
243
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	]);
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(* ------------------------------------------------------------------------ *)
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(* install simplifier for ('a)u                                             *)
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(* ------------------------------------------------------------------------ *)
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val lift_rews = [lift1,lift2,defined_up];
1274
ea0668a1c0ba added 8bit pragmas
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parents: 1267
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   350