author | clasohm |
Wed, 04 Oct 1995 14:01:44 +0100 | |
changeset 1267 | bca91b4e1710 |
parent 1168 | 74be52691d62 |
child 1274 | ea0668a1c0ba |
permissions | -rw-r--r-- |
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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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|
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Lemmas for lift3.thy |
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*) |
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|
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open Lift3; |
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|
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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 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 1), |
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(rtac (lub_const RS thelubI RS sym) 1), |
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(Asm_simp_tac 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 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 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 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 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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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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|
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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)" |
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(fn prems => |
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[ |
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(simp_tac (!simpset addsimps [cont_Iup]) 1), |
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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" |
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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 (!simpset addsimps [cont_Iup]) 1), |
163 |
(simp_tac (!simpset addsimps [cont_Iup]) 1) |
|
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]); |
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qed_goalw "defined_up" Lift3.thy [up_def] " up`x ~= UU" |
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(fn prems => |
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[ |
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(simp_tac (!simpset addsimps [cont_Iup]) 1), |
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(rtac defined_Iup2 1) |
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]); |
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qed_goalw "liftE1" Lift3.thy [up_def] |
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"[| p=UU ==> Q; !!x. p=up`x==>Q|] ==>Q" |
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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 (!simpset addsimps [cont_Iup]) 1) |
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]); |
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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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191 |
cont_Ilift2,cont2cont_CF1L]) 1)), |
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(rtac (beta_cfun RS ssubst) 1), |
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193 |
(REPEAT (resolve_tac (cont_lemmas @ [cont_Iup,cont_Ilift1, |
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cont_Ilift2,cont2cont_CF1L]) 1)), |
1267 | 195 |
(simp_tac (!simpset addsimps [cont_Iup,cont_Ilift1,cont_Ilift2]) 1) |
243
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]); |
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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), |
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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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(rtac (beta_cfun RS ssubst) 1), |
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(rtac cont_Ilift2 1), |
1267 | 208 |
(simp_tac (!simpset addsimps [cont_Iup,cont_Ilift1,cont_Ilift2]) 1) |
243
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]); |
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210 |
|
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211 |
qed_goalw "less_lift4b" Lift3.thy [up_def,lift_def] "~ up`x << UU" |
243
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(fn prems => |
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[ |
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(simp_tac (!simpset addsimps [cont_Iup]) 1), |
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(rtac less_lift3b 1) |
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216 |
]); |
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217 |
|
892 | 218 |
qed_goalw "less_lift4c" Lift3.thy [up_def,lift_def] |
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219 |
"(up`x << up`y) = (x<<y)" |
243
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(fn prems => |
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221 |
[ |
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(simp_tac (!simpset addsimps [cont_Iup]) 1), |
243
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(rtac less_lift2c 1) |
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224 |
]); |
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225 |
|
892 | 226 |
qed_goalw "thelub_lift2a" Lift3.thy [up_def,lift_def] |
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227 |
"[| is_chain(Y); ? i x. Y(i) = up`x |] ==>\ |
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228 |
\ 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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231 |
(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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234 |
cont_Ilift2,cont2cont_CF1L]) 1)), |
243
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(rtac (beta_cfun RS ssubst) 1), |
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236 |
(REPEAT (resolve_tac (cont_lemmas @ [cont_Iup,cont_Ilift1, |
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237 |
cont_Ilift2,cont2cont_CF1L]) 1)), |
243
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238 |
|
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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, |
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cont_Ilift2,cont2cont_CF1L]) 1)), |
243
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(rtac thelub_lift1a 1), |
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243 |
(atac 1), |
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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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(rtac exI 1), |
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(etac box_equals 1), |
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249 |
(rtac refl 1), |
1267 | 250 |
(simp_tac (!simpset addsimps [cont_Iup]) 1) |
243
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251 |
]); |
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252 |
|
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253 |
|
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254 |
|
892 | 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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257 |
(fn prems => |
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258 |
[ |
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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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262 |
(atac 1), |
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(strip_tac 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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264 |
(dtac spec 1), |
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265 |
(dtac spec 1), |
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(rtac swap 1), |
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(atac 1), |
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(dtac notnotD 1), |
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(etac box_equals 1), |
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(rtac refl 1), |
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(simp_tac (!simpset addsimps [cont_Iup]) 1) |
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]); |
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|
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|
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qed_goal "lift_lemma2" Lift3.thy " (? x.z = up`x) = (z~=UU)" |
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(fn prems => |
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[ |
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(rtac iffI 1), |
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(etac exE 1), |
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(hyp_subst_tac 1), |
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(rtac defined_up 1), |
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(res_inst_tac [("p","z")] liftE1 1), |
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(etac notE 1), |
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(atac 1), |
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(etac exI 1) |
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]); |
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|
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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" |
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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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(etac exI 1), |
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(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 | 303 |
qed_goal "thelub_lift2b_rev" Lift3.thy |
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"[| is_chain(Y); lub(range(Y)) = UU |] ==> ! i x. Y(i) ~= up`x" |
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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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(atac 1), |
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(atac 1) |
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]); |
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|
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|
892 | 319 |
qed_goal "thelub_lift3" Lift3.thy |
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"is_chain(Y) ==> lub(range(Y)) = UU |\ |
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\ lub(range(Y)) = up`(lub(range(%i. lift`(LAM x.x)`(Y i))))" |
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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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(rtac disjI1 2), |
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(rtac thelub_lift2b 2), |
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328 |
(atac 2), |
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329 |
(atac 2), |
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(rtac disjI2 2), |
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331 |
(rtac thelub_lift2a 2), |
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332 |
(atac 2), |
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(atac 2), |
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(fast_tac HOL_cs 1) |
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]); |
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|
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qed_goal "lift3" Lift3.thy "lift`up`x=x" |
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(fn prems => |
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339 |
[ |
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340 |
(res_inst_tac [("p","x")] liftE1 1), |
1267 | 341 |
(asm_simp_tac (!simpset addsimps [lift1,lift2]) 1), |
342 |
(asm_simp_tac (!simpset addsimps [lift1,lift2]) 1) |
|
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]); |
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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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|
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val lift_rews = [lift1,lift2,defined_up]; |