author | regensbu |
Thu, 29 Jun 1995 16:28:40 +0200 | |
changeset 1168 | 74be52691d62 |
parent 948 | 3647161d15d3 |
child 1267 | bca91b4e1710 |
permissions | -rw-r--r-- |
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(* Title: HOLCF/stream.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 stream.thy |
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*) |
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|
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open Stream; |
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(* ------------------------------------------------------------------------*) |
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(* The isomorphisms stream_rep_iso and stream_abs_iso are strict *) |
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(* ------------------------------------------------------------------------*) |
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|
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val stream_iso_strict= stream_rep_iso RS (stream_abs_iso RS |
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(allI RSN (2,allI RS iso_strict))); |
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val stream_rews = [stream_iso_strict RS conjunct1, |
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stream_iso_strict RS conjunct2]; |
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|
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(* ------------------------------------------------------------------------*) |
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(* Properties of stream_copy *) |
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(* ------------------------------------------------------------------------*) |
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|
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fun prover defs thm = prove_goalw Stream.thy defs thm |
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(fn prems => |
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[ |
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(cut_facts_tac prems 1), |
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(asm_simp_tac (HOLCF_ss addsimps |
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(stream_rews @ [stream_abs_iso,stream_rep_iso])) 1) |
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]); |
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val stream_copy = |
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[ |
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prover [stream_copy_def] "stream_copy`f`UU=UU", |
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prover [stream_copy_def,scons_def] |
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"x~=UU ==> stream_copy`f`(scons`x`xs)= scons`x`(f`xs)" |
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]; |
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val stream_rews = stream_copy @ stream_rews; |
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(* ------------------------------------------------------------------------*) |
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(* Exhaustion and elimination for streams *) |
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(* ------------------------------------------------------------------------*) |
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qed_goalw "Exh_stream" Stream.thy [scons_def] |
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"s = UU | (? x xs. x~=UU & s = scons`x`xs)" |
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(fn prems => |
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[ |
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(simp_tac HOLCF_ss 1), |
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(rtac (stream_rep_iso RS subst) 1), |
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(res_inst_tac [("p","stream_rep`s")] sprodE 1), |
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(asm_simp_tac (HOLCF_ss addsimps stream_rews) 1), |
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(asm_simp_tac HOLCF_ss 1), |
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(res_inst_tac [("p","y")] liftE1 1), |
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(contr_tac 1), |
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(rtac disjI2 1), |
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(rtac exI 1), |
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(rtac exI 1), |
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(etac conjI 1), |
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(asm_simp_tac HOLCF_ss 1) |
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]); |
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qed_goal "streamE" Stream.thy |
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"[| s=UU ==> Q; !!x xs.[|s=scons`x`xs;x~=UU|]==>Q|]==>Q" |
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(fn prems => |
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[ |
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(rtac (Exh_stream RS disjE) 1), |
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(eresolve_tac prems 1), |
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(etac exE 1), |
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(etac exE 1), |
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(resolve_tac prems 1), |
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(fast_tac HOL_cs 1), |
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(fast_tac HOL_cs 1) |
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]); |
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(* ------------------------------------------------------------------------*) |
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(* Properties of stream_when *) |
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(* ------------------------------------------------------------------------*) |
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fun prover defs thm = prove_goalw Stream.thy defs thm |
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(fn prems => |
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[ |
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(cut_facts_tac prems 1), |
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(asm_simp_tac (HOLCF_ss addsimps |
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(stream_rews @ [stream_abs_iso,stream_rep_iso])) 1) |
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]); |
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val stream_when = [ |
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prover [stream_when_def] "stream_when`f`UU=UU", |
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prover [stream_when_def,scons_def] |
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"x~=UU ==> stream_when`f`(scons`x`xs)= f`x`xs" |
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]; |
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val stream_rews = stream_when @ stream_rews; |
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(* ------------------------------------------------------------------------*) |
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(* Rewrites for discriminators and selectors *) |
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(* ------------------------------------------------------------------------*) |
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fun prover defs thm = prove_goalw Stream.thy defs thm |
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(fn prems => |
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[ |
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(simp_tac (HOLCF_ss addsimps stream_rews) 1) |
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]); |
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val stream_discsel = [ |
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prover [is_scons_def] "is_scons`UU=UU", |
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prover [shd_def] "shd`UU=UU", |
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prover [stl_def] "stl`UU=UU" |
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]; |
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fun prover defs thm = prove_goalw Stream.thy defs thm |
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(fn prems => |
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[ |
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(cut_facts_tac prems 1), |
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(asm_simp_tac (HOLCF_ss addsimps stream_rews) 1) |
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]); |
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val stream_discsel = [ |
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prover [is_scons_def,shd_def,stl_def] "x~=UU ==> is_scons`(scons`x`xs)=TT", |
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prover [is_scons_def,shd_def,stl_def] "x~=UU ==> shd`(scons`x`xs)=x", |
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prover [is_scons_def,shd_def,stl_def] "x~=UU ==> stl`(scons`x`xs)=xs" |
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] @ stream_discsel; |
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val stream_rews = stream_discsel @ stream_rews; |
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|
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(* ------------------------------------------------------------------------*) |
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(* Definedness and strictness *) |
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(* ------------------------------------------------------------------------*) |
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|
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fun prover contr thm = prove_goal Stream.thy thm |
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(fn prems => |
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[ |
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(res_inst_tac [("P1",contr)] classical3 1), |
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(simp_tac (HOLCF_ss addsimps stream_rews) 1), |
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(dtac sym 1), |
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(asm_simp_tac HOLCF_ss 1), |
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(simp_tac (HOLCF_ss addsimps (prems @ stream_rews)) 1) |
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141 |
]); |
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|
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val stream_constrdef = [ |
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prover "is_scons`(UU::'a stream)~=UU" "x~=UU ==> scons`(x::'a)`xs~=UU" |
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]; |
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|
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fun prover defs thm = prove_goalw Stream.thy defs thm |
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(fn prems => |
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149 |
[ |
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(simp_tac (HOLCF_ss addsimps stream_rews) 1) |
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151 |
]); |
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152 |
|
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val stream_constrdef = [ |
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prover [scons_def] "scons`UU`xs=UU" |
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] @ stream_constrdef; |
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|
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val stream_rews = stream_constrdef @ stream_rews; |
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|
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|
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(* ------------------------------------------------------------------------*) |
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(* Distinctness wrt. << and = *) |
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(* ------------------------------------------------------------------------*) |
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|
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|
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(* ------------------------------------------------------------------------*) |
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(* Invertibility *) |
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(* ------------------------------------------------------------------------*) |
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|
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val stream_invert = |
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[ |
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prove_goal Stream.thy "[|x1~=UU; y1~=UU;\ |
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\ scons`x1`x2 << scons`y1`y2|] ==> x1<< y1 & x2 << y2" |
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(fn prems => |
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[ |
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(cut_facts_tac prems 1), |
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(rtac conjI 1), |
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(dres_inst_tac [("fo5","stream_when`(LAM x l.x)")] monofun_cfun_arg 1), |
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(etac box_less 1), |
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(asm_simp_tac (HOLCF_ss addsimps stream_when) 1), |
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(asm_simp_tac (HOLCF_ss addsimps stream_when) 1), |
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(dres_inst_tac [("fo5","stream_when`(LAM x l.l)")] monofun_cfun_arg 1), |
243
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182 |
(etac box_less 1), |
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183 |
(asm_simp_tac (HOLCF_ss addsimps stream_when) 1), |
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184 |
(asm_simp_tac (HOLCF_ss addsimps stream_when) 1) |
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185 |
]) |
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186 |
]; |
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|
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(* ------------------------------------------------------------------------*) |
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189 |
(* Injectivity *) |
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(* ------------------------------------------------------------------------*) |
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191 |
|
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192 |
val stream_inject = |
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193 |
[ |
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194 |
prove_goal Stream.thy "[|x1~=UU; y1~=UU;\ |
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\ scons`x1`x2 = scons`y1`y2 |] ==> x1= y1 & x2 = y2" |
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(fn prems => |
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197 |
[ |
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(cut_facts_tac prems 1), |
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199 |
(rtac conjI 1), |
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200 |
(dres_inst_tac [("f","stream_when`(LAM x l.x)")] cfun_arg_cong 1), |
243
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201 |
(etac box_equals 1), |
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202 |
(asm_simp_tac (HOLCF_ss addsimps stream_when) 1), |
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203 |
(asm_simp_tac (HOLCF_ss addsimps stream_when) 1), |
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204 |
(dres_inst_tac [("f","stream_when`(LAM x l.l)")] cfun_arg_cong 1), |
243
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205 |
(etac box_equals 1), |
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206 |
(asm_simp_tac (HOLCF_ss addsimps stream_when) 1), |
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207 |
(asm_simp_tac (HOLCF_ss addsimps stream_when) 1) |
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208 |
]) |
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209 |
]; |
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210 |
|
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211 |
(* ------------------------------------------------------------------------*) |
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212 |
(* definedness for discriminators and selectors *) |
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213 |
(* ------------------------------------------------------------------------*) |
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214 |
|
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215 |
fun prover thm = prove_goal Stream.thy thm |
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216 |
(fn prems => |
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217 |
[ |
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218 |
(cut_facts_tac prems 1), |
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219 |
(rtac streamE 1), |
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220 |
(contr_tac 1), |
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221 |
(REPEAT (asm_simp_tac (HOLCF_ss addsimps stream_discsel) 1)) |
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222 |
]); |
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223 |
|
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224 |
val stream_discsel_def = |
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225 |
[ |
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226 |
prover "s~=UU ==> is_scons`s ~= UU", |
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227 |
prover "s~=UU ==> shd`s ~=UU" |
243
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228 |
]; |
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229 |
|
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230 |
val stream_rews = stream_discsel_def @ stream_rews; |
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231 |
|
297 | 232 |
|
243
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233 |
(* ------------------------------------------------------------------------*) |
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234 |
(* Properties stream_take *) |
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235 |
(* ------------------------------------------------------------------------*) |
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236 |
|
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237 |
val stream_take = |
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238 |
[ |
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239 |
prove_goalw Stream.thy [stream_take_def] "stream_take n`UU = UU" |
243
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240 |
(fn prems => |
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|
241 |
[ |
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242 |
(res_inst_tac [("n","n")] natE 1), |
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243 |
(asm_simp_tac iterate_ss 1), |
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244 |
(asm_simp_tac iterate_ss 1), |
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245 |
(simp_tac (HOLCF_ss addsimps stream_rews) 1) |
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246 |
]), |
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247 |
prove_goalw Stream.thy [stream_take_def] "stream_take 0`xs=UU" |
243
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248 |
(fn prems => |
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249 |
[ |
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250 |
(asm_simp_tac iterate_ss 1) |
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251 |
])]; |
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252 |
|
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253 |
fun prover thm = prove_goalw Stream.thy [stream_take_def] thm |
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254 |
(fn prems => |
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255 |
[ |
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256 |
(cut_facts_tac prems 1), |
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(simp_tac iterate_ss 1), |
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258 |
(asm_simp_tac (HOLCF_ss addsimps stream_rews) 1) |
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259 |
]); |
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260 |
|
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261 |
val stream_take = [ |
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262 |
prover |
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263 |
"x~=UU ==> stream_take (Suc n)`(scons`x`xs) = scons`x`(stream_take n`xs)" |
243
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264 |
] @ stream_take; |
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265 |
|
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266 |
val stream_rews = stream_take @ stream_rews; |
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267 |
|
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268 |
(* ------------------------------------------------------------------------*) |
297 | 269 |
(* enhance the simplifier *) |
270 |
(* ------------------------------------------------------------------------*) |
|
271 |
||
892 | 272 |
qed_goal "stream_copy2" Stream.thy |
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273 |
"stream_copy`f`(scons`x`xs) = scons`x`(f`xs)" |
297 | 274 |
(fn prems => |
275 |
[ |
|
276 |
(res_inst_tac [("Q","x=UU")] classical2 1), |
|
277 |
(asm_simp_tac (HOLCF_ss addsimps stream_rews) 1), |
|
278 |
(asm_simp_tac (HOLCF_ss addsimps stream_rews) 1) |
|
279 |
]); |
|
280 |
||
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281 |
qed_goal "shd2" Stream.thy "shd`(scons`x`xs) = x" |
297 | 282 |
(fn prems => |
283 |
[ |
|
284 |
(res_inst_tac [("Q","x=UU")] classical2 1), |
|
285 |
(asm_simp_tac (HOLCF_ss addsimps stream_rews) 1), |
|
286 |
(asm_simp_tac (HOLCF_ss addsimps stream_rews) 1) |
|
287 |
]); |
|
288 |
||
892 | 289 |
qed_goal "stream_take2" Stream.thy |
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290 |
"stream_take (Suc n)`(scons`x`xs) = scons`x`(stream_take n`xs)" |
297 | 291 |
(fn prems => |
292 |
[ |
|
293 |
(res_inst_tac [("Q","x=UU")] classical2 1), |
|
294 |
(asm_simp_tac (HOLCF_ss addsimps stream_rews) 1), |
|
295 |
(asm_simp_tac (HOLCF_ss addsimps stream_rews) 1) |
|
296 |
]); |
|
297 |
||
298 |
val stream_rews = [stream_iso_strict RS conjunct1, |
|
299 |
stream_iso_strict RS conjunct2, |
|
300 |
hd stream_copy, stream_copy2] |
|
301 |
@ stream_when |
|
302 |
@ [hd stream_discsel,shd2] @ (tl (tl stream_discsel)) |
|
303 |
@ stream_constrdef |
|
304 |
@ stream_discsel_def |
|
305 |
@ [ stream_take2] @ (tl stream_take); |
|
306 |
||
307 |
||
308 |
(* ------------------------------------------------------------------------*) |
|
243
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(* take lemma for streams *) |
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310 |
(* ------------------------------------------------------------------------*) |
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311 |
|
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312 |
fun prover reach defs thm = prove_goalw Stream.thy defs thm |
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313 |
(fn prems => |
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314 |
[ |
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315 |
(res_inst_tac [("t","s1")] (reach RS subst) 1), |
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316 |
(res_inst_tac [("t","s2")] (reach RS subst) 1), |
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317 |
(rtac (fix_def2 RS ssubst) 1), |
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318 |
(rtac (contlub_cfun_fun RS ssubst) 1), |
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319 |
(rtac is_chain_iterate 1), |
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320 |
(rtac (contlub_cfun_fun RS ssubst) 1), |
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321 |
(rtac is_chain_iterate 1), |
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322 |
(rtac lub_equal 1), |
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323 |
(rtac (is_chain_iterate RS ch2ch_fappL) 1), |
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324 |
(rtac (is_chain_iterate RS ch2ch_fappL) 1), |
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325 |
(rtac allI 1), |
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326 |
(resolve_tac prems 1) |
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327 |
]); |
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328 |
|
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329 |
val stream_take_lemma = prover stream_reach [stream_take_def] |
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330 |
"(!!n.stream_take n`s1 = stream_take n`s2) ==> s1=s2"; |
243
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331 |
|
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332 |
|
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333 |
qed_goal "stream_reach2" Stream.thy "lub(range(%i.stream_take i`s))=s" |
430 | 334 |
(fn prems => |
335 |
[ |
|
336 |
(res_inst_tac [("t","s")] (stream_reach RS subst) 1), |
|
337 |
(rtac (fix_def2 RS ssubst) 1), |
|
338 |
(rewrite_goals_tac [stream_take_def]), |
|
339 |
(rtac (contlub_cfun_fun RS ssubst) 1), |
|
340 |
(rtac is_chain_iterate 1), |
|
341 |
(rtac refl 1) |
|
342 |
]); |
|
343 |
||
243
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344 |
(* ------------------------------------------------------------------------*) |
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345 |
(* Co -induction for streams *) |
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346 |
(* ------------------------------------------------------------------------*) |
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347 |
|
892 | 348 |
qed_goalw "stream_coind_lemma" Stream.thy [stream_bisim_def] |
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349 |
"stream_bisim R ==> ! p q. R p q --> stream_take n`p = stream_take n`q" |
243
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350 |
(fn prems => |
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351 |
[ |
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352 |
(cut_facts_tac prems 1), |
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|
353 |
(nat_ind_tac "n" 1), |
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|
354 |
(simp_tac (HOLCF_ss addsimps stream_rews) 1), |
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|
355 |
(strip_tac 1), |
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|
356 |
((etac allE 1) THEN (etac allE 1) THEN (etac (mp RS disjE) 1)), |
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|
357 |
(atac 1), |
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|
358 |
(asm_simp_tac (HOLCF_ss addsimps stream_rews) 1), |
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|
359 |
(etac exE 1), |
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|
360 |
(etac exE 1), |
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|
361 |
(etac exE 1), |
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|
362 |
(asm_simp_tac (HOLCF_ss addsimps stream_rews) 1), |
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|
363 |
(REPEAT (etac conjE 1)), |
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|
364 |
(rtac cfun_arg_cong 1), |
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|
365 |
(fast_tac HOL_cs 1) |
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|
366 |
]); |
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|
367 |
|
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|
368 |
qed_goal "stream_coind" Stream.thy "[|stream_bisim R ;R p q|] ==> p = q" |
243
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|
369 |
(fn prems => |
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|
370 |
[ |
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|
371 |
(rtac stream_take_lemma 1), |
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|
372 |
(rtac (stream_coind_lemma RS spec RS spec RS mp) 1), |
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|
373 |
(resolve_tac prems 1), |
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|
374 |
(resolve_tac prems 1) |
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|
375 |
]); |
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|
376 |
|
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377 |
(* ------------------------------------------------------------------------*) |
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|
378 |
(* structural induction for admissible predicates *) |
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|
379 |
(* ------------------------------------------------------------------------*) |
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|
380 |
|
892 | 381 |
qed_goal "stream_finite_ind" Stream.thy |
297 | 382 |
"[|P(UU);\ |
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|
383 |
\ !! x s1.[|x~=UU;P(s1)|] ==> P(scons`x`s1)\ |
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|
384 |
\ |] ==> !s.P(stream_take n`s)" |
297 | 385 |
(fn prems => |
386 |
[ |
|
387 |
(nat_ind_tac "n" 1), |
|
388 |
(simp_tac (HOLCF_ss addsimps stream_rews) 1), |
|
389 |
(resolve_tac prems 1), |
|
390 |
(rtac allI 1), |
|
391 |
(res_inst_tac [("s","s")] streamE 1), |
|
392 |
(asm_simp_tac (HOLCF_ss addsimps stream_rews) 1), |
|
393 |
(resolve_tac prems 1), |
|
394 |
(asm_simp_tac (HOLCF_ss addsimps stream_rews) 1), |
|
395 |
(resolve_tac prems 1), |
|
396 |
(atac 1), |
|
397 |
(etac spec 1) |
|
398 |
]); |
|
399 |
||
892 | 400 |
qed_goalw "stream_finite_ind2" Stream.thy [stream_finite_def] |
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changeset
|
401 |
"(!!n.P(stream_take n`s)) ==> stream_finite(s) -->P(s)" |
297 | 402 |
(fn prems => |
403 |
[ |
|
404 |
(strip_tac 1), |
|
405 |
(etac exE 1), |
|
406 |
(etac subst 1), |
|
407 |
(resolve_tac prems 1) |
|
408 |
]); |
|
409 |
||
892 | 410 |
qed_goal "stream_finite_ind3" Stream.thy |
297 | 411 |
"[|P(UU);\ |
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74be52691d62
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changeset
|
412 |
\ !! x s1.[|x~=UU;P(s1)|] ==> P(scons`x`s1)\ |
297 | 413 |
\ |] ==> stream_finite(s) --> P(s)" |
414 |
(fn prems => |
|
415 |
[ |
|
416 |
(rtac stream_finite_ind2 1), |
|
417 |
(rtac (stream_finite_ind RS spec) 1), |
|
418 |
(REPEAT (resolve_tac prems 1)), |
|
419 |
(REPEAT (atac 1)) |
|
420 |
]); |
|
421 |
||
625 | 422 |
(* prove induction using definition of admissibility |
423 |
stream_reach rsp. stream_reach2 |
|
424 |
and finite induction stream_finite_ind *) |
|
425 |
||
892 | 426 |
qed_goal "stream_ind" Stream.thy |
625 | 427 |
"[|adm(P);\ |
428 |
\ P(UU);\ |
|
1168
74be52691d62
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|
429 |
\ !! x s1.[|x~=UU;P(s1)|] ==> P(scons`x`s1)\ |
625 | 430 |
\ |] ==> P(s)" |
431 |
(fn prems => |
|
432 |
[ |
|
433 |
(rtac (stream_reach2 RS subst) 1), |
|
434 |
(rtac (adm_def2 RS iffD1 RS spec RS mp RS mp) 1), |
|
435 |
(resolve_tac prems 1), |
|
436 |
(SELECT_GOAL (rewrite_goals_tac [stream_take_def]) 1), |
|
437 |
(rtac ch2ch_fappL 1), |
|
438 |
(rtac is_chain_iterate 1), |
|
439 |
(rtac allI 1), |
|
440 |
(rtac (stream_finite_ind RS spec) 1), |
|
441 |
(REPEAT (resolve_tac prems 1)), |
|
442 |
(REPEAT (atac 1)) |
|
443 |
]); |
|
444 |
||
445 |
(* prove induction with usual LCF-Method using fixed point induction *) |
|
892 | 446 |
qed_goal "stream_ind" Stream.thy |
297 | 447 |
"[|adm(P);\ |
243
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|
448 |
\ P(UU);\ |
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|
449 |
\ !! x s1.[|x~=UU;P(s1)|] ==> P(scons`x`s1)\ |
243
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|
450 |
\ |] ==> P(s)" |
c22b85994e17
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|
451 |
(fn prems => |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
452 |
[ |
c22b85994e17
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|
453 |
(rtac (stream_reach RS subst) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
454 |
(res_inst_tac [("x","s")] spec 1), |
297 | 455 |
(rtac wfix_ind 1), |
456 |
(rtac adm_impl_admw 1), |
|
457 |
(REPEAT (resolve_tac adm_thms 1)), |
|
243
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|
458 |
(rtac adm_subst 1), |
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The curried version of HOLCF is now just called HOLCF. The old
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parents:
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changeset
|
459 |
(cont_tacR 1), |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
460 |
(resolve_tac prems 1), |
297 | 461 |
(rtac allI 1), |
462 |
(rtac (rewrite_rule [stream_take_def] stream_finite_ind) 1), |
|
463 |
(REPEAT (resolve_tac prems 1)), |
|
464 |
(REPEAT (atac 1)) |
|
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
465 |
]); |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
466 |
|
625 | 467 |
|
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
468 |
(* ------------------------------------------------------------------------*) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
469 |
(* simplify use of Co-induction *) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
470 |
(* ------------------------------------------------------------------------*) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
471 |
|
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
948
diff
changeset
|
472 |
qed_goal "surjectiv_scons" Stream.thy "scons`(shd`s)`(stl`s)=s" |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
473 |
(fn prems => |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
474 |
[ |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
475 |
(res_inst_tac [("s","s")] streamE 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
476 |
(asm_simp_tac (HOLCF_ss addsimps stream_rews) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
477 |
(asm_simp_tac (HOLCF_ss addsimps stream_rews) 1) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
478 |
]); |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
479 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
480 |
|
892 | 481 |
qed_goalw "stream_coind_lemma2" Stream.thy [stream_bisim_def] |
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
948
diff
changeset
|
482 |
"!s1 s2. R s1 s2 --> shd`s1 = shd`s2 & R (stl`s1) (stl`s2) ==> stream_bisim R" |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
483 |
(fn prems => |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
484 |
[ |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
485 |
(cut_facts_tac prems 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
486 |
(strip_tac 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
487 |
(etac allE 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
488 |
(etac allE 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
489 |
(dtac mp 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
490 |
(atac 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
491 |
(etac conjE 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
492 |
(res_inst_tac [("Q","s1 = UU & s2 = UU")] classical2 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
493 |
(rtac disjI1 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
494 |
(fast_tac HOL_cs 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
495 |
(rtac disjI2 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
496 |
(rtac disjE 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
497 |
(etac (de_morgan2 RS ssubst) 1), |
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
948
diff
changeset
|
498 |
(res_inst_tac [("x","shd`s1")] exI 1), |
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
948
diff
changeset
|
499 |
(res_inst_tac [("x","stl`s1")] exI 1), |
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
948
diff
changeset
|
500 |
(res_inst_tac [("x","stl`s2")] exI 1), |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
501 |
(rtac conjI 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
502 |
(eresolve_tac stream_discsel_def 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
503 |
(asm_simp_tac (HOLCF_ss addsimps stream_rews addsimps [surjectiv_scons]) 1), |
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
948
diff
changeset
|
504 |
(eres_inst_tac [("s","shd`s1"),("t","shd`s2")] subst 1), |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
505 |
(simp_tac (HOLCF_ss addsimps stream_rews addsimps [surjectiv_scons]) 1), |
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
948
diff
changeset
|
506 |
(res_inst_tac [("x","shd`s2")] exI 1), |
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
948
diff
changeset
|
507 |
(res_inst_tac [("x","stl`s1")] exI 1), |
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
948
diff
changeset
|
508 |
(res_inst_tac [("x","stl`s2")] exI 1), |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
509 |
(rtac conjI 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
510 |
(eresolve_tac stream_discsel_def 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
511 |
(asm_simp_tac (HOLCF_ss addsimps stream_rews addsimps [surjectiv_scons]) 1), |
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
948
diff
changeset
|
512 |
(res_inst_tac [("s","shd`s1"),("t","shd`s2")] ssubst 1), |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
513 |
(etac sym 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
514 |
(simp_tac (HOLCF_ss addsimps stream_rews addsimps [surjectiv_scons]) 1) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
515 |
]); |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
516 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
517 |
|
297 | 518 |
(* ------------------------------------------------------------------------*) |
519 |
(* theorems about finite and infinite streams *) |
|
520 |
(* ------------------------------------------------------------------------*) |
|
521 |
||
522 |
(* ----------------------------------------------------------------------- *) |
|
523 |
(* 2 lemmas about stream_finite *) |
|
524 |
(* ----------------------------------------------------------------------- *) |
|
525 |
||
892 | 526 |
qed_goalw "stream_finite_UU" Stream.thy [stream_finite_def] |
297 | 527 |
"stream_finite(UU)" |
528 |
(fn prems => |
|
529 |
[ |
|
530 |
(rtac exI 1), |
|
531 |
(simp_tac (HOLCF_ss addsimps stream_rews) 1) |
|
532 |
]); |
|
533 |
||
892 | 534 |
qed_goal "inf_stream_not_UU" Stream.thy "~stream_finite(s) ==> s ~= UU" |
297 | 535 |
(fn prems => |
536 |
[ |
|
537 |
(cut_facts_tac prems 1), |
|
538 |
(etac swap 1), |
|
539 |
(dtac notnotD 1), |
|
540 |
(hyp_subst_tac 1), |
|
541 |
(rtac stream_finite_UU 1) |
|
542 |
]); |
|
543 |
||
544 |
(* ----------------------------------------------------------------------- *) |
|
545 |
(* a lemma about shd *) |
|
546 |
(* ----------------------------------------------------------------------- *) |
|
547 |
||
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
948
diff
changeset
|
548 |
qed_goal "stream_shd_lemma1" Stream.thy "shd`s=UU --> s=UU" |
297 | 549 |
(fn prems => |
550 |
[ |
|
551 |
(res_inst_tac [("s","s")] streamE 1), |
|
552 |
(asm_simp_tac (HOLCF_ss addsimps stream_rews) 1), |
|
553 |
(hyp_subst_tac 1), |
|
554 |
(asm_simp_tac (HOLCF_ss addsimps stream_rews) 1) |
|
555 |
]); |
|
556 |
||
557 |
||
558 |
(* ----------------------------------------------------------------------- *) |
|
559 |
(* lemmas about stream_take *) |
|
560 |
(* ----------------------------------------------------------------------- *) |
|
561 |
||
892 | 562 |
qed_goal "stream_take_lemma1" Stream.thy |
297 | 563 |
"!x xs.x~=UU --> \ |
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
948
diff
changeset
|
564 |
\ stream_take (Suc n)`(scons`x`xs) = scons`x`xs --> stream_take n`xs=xs" |
297 | 565 |
(fn prems => |
566 |
[ |
|
567 |
(rtac allI 1), |
|
568 |
(rtac allI 1), |
|
569 |
(rtac impI 1), |
|
570 |
(asm_simp_tac (HOLCF_ss addsimps stream_rews) 1), |
|
571 |
(strip_tac 1), |
|
572 |
(rtac ((hd stream_inject) RS conjunct2) 1), |
|
573 |
(atac 1), |
|
574 |
(atac 1), |
|
575 |
(atac 1) |
|
576 |
]); |
|
577 |
||
578 |
||
892 | 579 |
qed_goal "stream_take_lemma2" Stream.thy |
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
948
diff
changeset
|
580 |
"! s2. stream_take n`s2 = s2 --> stream_take (Suc n)`s2=s2" |
297 | 581 |
(fn prems => |
582 |
[ |
|
583 |
(nat_ind_tac "n" 1), |
|
584 |
(simp_tac (HOLCF_ss addsimps stream_rews) 1), |
|
585 |
(strip_tac 1 ), |
|
586 |
(hyp_subst_tac 1), |
|
587 |
(simp_tac (HOLCF_ss addsimps stream_rews) 1), |
|
588 |
(rtac allI 1), |
|
589 |
(res_inst_tac [("s","s2")] streamE 1), |
|
590 |
(asm_simp_tac (HOLCF_ss addsimps stream_rews) 1), |
|
591 |
(asm_simp_tac (HOLCF_ss addsimps stream_rews) 1), |
|
592 |
(strip_tac 1 ), |
|
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
948
diff
changeset
|
593 |
(subgoal_tac "stream_take n1`xs = xs" 1), |
297 | 594 |
(rtac ((hd stream_inject) RS conjunct2) 2), |
595 |
(atac 4), |
|
596 |
(atac 2), |
|
597 |
(atac 2), |
|
598 |
(rtac cfun_arg_cong 1), |
|
599 |
(fast_tac HOL_cs 1) |
|
600 |
]); |
|
601 |
||
892 | 602 |
qed_goal "stream_take_lemma3" Stream.thy |
297 | 603 |
"!x xs.x~=UU --> \ |
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
948
diff
changeset
|
604 |
\ stream_take n`(scons`x`xs) = scons`x`xs --> stream_take n`xs=xs" |
297 | 605 |
(fn prems => |
606 |
[ |
|
607 |
(nat_ind_tac "n" 1), |
|
608 |
(asm_simp_tac (HOLCF_ss addsimps stream_rews) 1), |
|
609 |
(strip_tac 1 ), |
|
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
948
diff
changeset
|
610 |
(res_inst_tac [("P","scons`x`xs=UU")] notE 1), |
297 | 611 |
(eresolve_tac stream_constrdef 1), |
612 |
(etac sym 1), |
|
613 |
(strip_tac 1 ), |
|
614 |
(rtac (stream_take_lemma2 RS spec RS mp) 1), |
|
615 |
(res_inst_tac [("x1.1","x")] ((hd stream_inject) RS conjunct2) 1), |
|
616 |
(atac 1), |
|
617 |
(atac 1), |
|
618 |
(etac (stream_take2 RS subst) 1) |
|
619 |
]); |
|
620 |
||
892 | 621 |
qed_goal "stream_take_lemma4" Stream.thy |
297 | 622 |
"!x xs.\ |
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
948
diff
changeset
|
623 |
\stream_take n`xs=xs --> stream_take (Suc n)`(scons`x`xs) = scons`x`xs" |
297 | 624 |
(fn prems => |
625 |
[ |
|
626 |
(nat_ind_tac "n" 1), |
|
627 |
(simp_tac (HOLCF_ss addsimps stream_rews) 1), |
|
628 |
(simp_tac (HOLCF_ss addsimps stream_rews) 1) |
|
629 |
]); |
|
630 |
||
631 |
(* ---- *) |
|
632 |
||
892 | 633 |
qed_goal "stream_take_lemma5" Stream.thy |
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
948
diff
changeset
|
634 |
"!s. stream_take n`s=s --> iterate n stl s=UU" |
297 | 635 |
(fn prems => |
636 |
[ |
|
637 |
(nat_ind_tac "n" 1), |
|
638 |
(simp_tac iterate_ss 1), |
|
639 |
(simp_tac (HOLCF_ss addsimps stream_rews) 1), |
|
640 |
(strip_tac 1), |
|
641 |
(res_inst_tac [("s","s")] streamE 1), |
|
642 |
(hyp_subst_tac 1), |
|
643 |
(rtac (iterate_Suc2 RS ssubst) 1), |
|
644 |
(asm_simp_tac (HOLCF_ss addsimps stream_rews) 1), |
|
645 |
(rtac (iterate_Suc2 RS ssubst) 1), |
|
646 |
(asm_simp_tac (HOLCF_ss addsimps stream_rews) 1), |
|
647 |
(etac allE 1), |
|
648 |
(etac mp 1), |
|
649 |
(hyp_subst_tac 1), |
|
650 |
(etac (stream_take_lemma1 RS spec RS spec RS mp RS mp) 1), |
|
651 |
(atac 1) |
|
652 |
]); |
|
653 |
||
892 | 654 |
qed_goal "stream_take_lemma6" Stream.thy |
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
948
diff
changeset
|
655 |
"!s.iterate n stl s =UU --> stream_take n`s=s" |
297 | 656 |
(fn prems => |
657 |
[ |
|
658 |
(nat_ind_tac "n" 1), |
|
659 |
(simp_tac iterate_ss 1), |
|
660 |
(strip_tac 1), |
|
661 |
(asm_simp_tac (HOLCF_ss addsimps stream_rews) 1), |
|
662 |
(rtac allI 1), |
|
663 |
(res_inst_tac [("s","s")] streamE 1), |
|
664 |
(hyp_subst_tac 1), |
|
665 |
(asm_simp_tac (HOLCF_ss addsimps stream_rews) 1), |
|
666 |
(hyp_subst_tac 1), |
|
667 |
(rtac (iterate_Suc2 RS ssubst) 1), |
|
668 |
(asm_simp_tac (HOLCF_ss addsimps stream_rews) 1) |
|
669 |
]); |
|
670 |
||
892 | 671 |
qed_goal "stream_take_lemma7" Stream.thy |
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
948
diff
changeset
|
672 |
"(iterate n stl s=UU) = (stream_take n`s=s)" |
297 | 673 |
(fn prems => |
674 |
[ |
|
675 |
(rtac iffI 1), |
|
676 |
(etac (stream_take_lemma6 RS spec RS mp) 1), |
|
677 |
(etac (stream_take_lemma5 RS spec RS mp) 1) |
|
678 |
]); |
|
679 |
||
680 |
||
892 | 681 |
qed_goal "stream_take_lemma8" Stream.thy |
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
948
diff
changeset
|
682 |
"[|adm(P); !n. ? m. n < m & P (stream_take m`s)|] ==> P(s)" |
430 | 683 |
(fn prems => |
684 |
[ |
|
685 |
(cut_facts_tac prems 1), |
|
686 |
(rtac (stream_reach2 RS subst) 1), |
|
687 |
(rtac adm_disj_lemma11 1), |
|
688 |
(atac 1), |
|
689 |
(atac 2), |
|
690 |
(rewrite_goals_tac [stream_take_def]), |
|
691 |
(rtac ch2ch_fappL 1), |
|
692 |
(rtac is_chain_iterate 1) |
|
693 |
]); |
|
694 |
||
297 | 695 |
(* ----------------------------------------------------------------------- *) |
696 |
(* lemmas stream_finite *) |
|
697 |
(* ----------------------------------------------------------------------- *) |
|
698 |
||
892 | 699 |
qed_goalw "stream_finite_lemma1" Stream.thy [stream_finite_def] |
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
948
diff
changeset
|
700 |
"stream_finite(xs) ==> stream_finite(scons`x`xs)" |
297 | 701 |
(fn prems => |
702 |
[ |
|
703 |
(cut_facts_tac prems 1), |
|
704 |
(etac exE 1), |
|
705 |
(rtac exI 1), |
|
706 |
(etac (stream_take_lemma4 RS spec RS spec RS mp) 1) |
|
707 |
]); |
|
708 |
||
892 | 709 |
qed_goalw "stream_finite_lemma2" Stream.thy [stream_finite_def] |
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
948
diff
changeset
|
710 |
"[|x~=UU; stream_finite(scons`x`xs)|] ==> stream_finite(xs)" |
297 | 711 |
(fn prems => |
712 |
[ |
|
713 |
(cut_facts_tac prems 1), |
|
714 |
(etac exE 1), |
|
715 |
(rtac exI 1), |
|
716 |
(etac (stream_take_lemma3 RS spec RS spec RS mp RS mp) 1), |
|
717 |
(atac 1) |
|
718 |
]); |
|
719 |
||
892 | 720 |
qed_goal "stream_finite_lemma3" Stream.thy |
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
948
diff
changeset
|
721 |
"x~=UU ==> stream_finite(scons`x`xs) = stream_finite(xs)" |
297 | 722 |
(fn prems => |
723 |
[ |
|
724 |
(cut_facts_tac prems 1), |
|
725 |
(rtac iffI 1), |
|
726 |
(etac stream_finite_lemma2 1), |
|
727 |
(atac 1), |
|
728 |
(etac stream_finite_lemma1 1) |
|
729 |
]); |
|
730 |
||
731 |
||
892 | 732 |
qed_goalw "stream_finite_lemma5" Stream.thy [stream_finite_def] |
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
948
diff
changeset
|
733 |
"(!n. s1 << s2 --> stream_take n`s2 = s2 --> stream_finite(s1))\ |
297 | 734 |
\=(s1 << s2 --> stream_finite(s2) --> stream_finite(s1))" |
735 |
(fn prems => |
|
736 |
[ |
|
737 |
(rtac iffI 1), |
|
738 |
(fast_tac HOL_cs 1), |
|
739 |
(fast_tac HOL_cs 1) |
|
740 |
]); |
|
741 |
||
892 | 742 |
qed_goal "stream_finite_lemma6" Stream.thy |
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
948
diff
changeset
|
743 |
"!s1 s2. s1 << s2 --> stream_take n`s2 = s2 --> stream_finite(s1)" |
297 | 744 |
(fn prems => |
745 |
[ |
|
746 |
(nat_ind_tac "n" 1), |
|
747 |
(simp_tac (HOLCF_ss addsimps stream_rews) 1), |
|
748 |
(strip_tac 1 ), |
|
749 |
(hyp_subst_tac 1), |
|
750 |
(dtac UU_I 1), |
|
751 |
(hyp_subst_tac 1), |
|
752 |
(rtac stream_finite_UU 1), |
|
753 |
(rtac allI 1), |
|
754 |
(rtac allI 1), |
|
755 |
(res_inst_tac [("s","s1")] streamE 1), |
|
756 |
(hyp_subst_tac 1), |
|
757 |
(strip_tac 1 ), |
|
758 |
(rtac stream_finite_UU 1), |
|
759 |
(hyp_subst_tac 1), |
|
760 |
(res_inst_tac [("s","s2")] streamE 1), |
|
761 |
(hyp_subst_tac 1), |
|
762 |
(strip_tac 1 ), |
|
763 |
(dtac UU_I 1), |
|
764 |
(asm_simp_tac(HOLCF_ss addsimps (stream_rews @ [stream_finite_UU])) 1), |
|
765 |
(hyp_subst_tac 1), |
|
766 |
(simp_tac (HOLCF_ss addsimps stream_rews) 1), |
|
767 |
(strip_tac 1 ), |
|
768 |
(rtac stream_finite_lemma1 1), |
|
769 |
(subgoal_tac "xs << xsa" 1), |
|
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
948
diff
changeset
|
770 |
(subgoal_tac "stream_take n1`xsa = xsa" 1), |
297 | 771 |
(fast_tac HOL_cs 1), |
772 |
(res_inst_tac [("x1.1","xa"),("y1.1","xa")] |
|
773 |
((hd stream_inject) RS conjunct2) 1), |
|
774 |
(atac 1), |
|
775 |
(atac 1), |
|
776 |
(atac 1), |
|
777 |
(res_inst_tac [("x1.1","x"),("y1.1","xa")] |
|
778 |
((hd stream_invert) RS conjunct2) 1), |
|
779 |
(atac 1), |
|
780 |
(atac 1), |
|
781 |
(atac 1) |
|
782 |
]); |
|
783 |
||
892 | 784 |
qed_goal "stream_finite_lemma7" Stream.thy |
297 | 785 |
"s1 << s2 --> stream_finite(s2) --> stream_finite(s1)" |
786 |
(fn prems => |
|
787 |
[ |
|
788 |
(rtac (stream_finite_lemma5 RS iffD1) 1), |
|
789 |
(rtac allI 1), |
|
790 |
(rtac (stream_finite_lemma6 RS spec RS spec) 1) |
|
791 |
]); |
|
792 |
||
892 | 793 |
qed_goalw "stream_finite_lemma8" Stream.thy [stream_finite_def] |
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
948
diff
changeset
|
794 |
"stream_finite(s) = (? n. iterate n stl s = UU)" |
297 | 795 |
(fn prems => |
796 |
[ |
|
797 |
(simp_tac (HOL_ss addsimps [stream_take_lemma7]) 1) |
|
798 |
]); |
|
799 |
||
800 |
||
801 |
(* ----------------------------------------------------------------------- *) |
|
802 |
(* admissibility of ~stream_finite *) |
|
803 |
(* ----------------------------------------------------------------------- *) |
|
804 |
||
892 | 805 |
qed_goalw "adm_not_stream_finite" Stream.thy [adm_def] |
297 | 806 |
"adm(%s. ~ stream_finite(s))" |
807 |
(fn prems => |
|
808 |
[ |
|
809 |
(strip_tac 1 ), |
|
810 |
(res_inst_tac [("P1","!i. ~ stream_finite(Y(i))")] classical3 1), |
|
811 |
(atac 2), |
|
812 |
(subgoal_tac "!i.stream_finite(Y(i))" 1), |
|
813 |
(fast_tac HOL_cs 1), |
|
814 |
(rtac allI 1), |
|
815 |
(rtac (stream_finite_lemma7 RS mp RS mp) 1), |
|
816 |
(etac is_ub_thelub 1), |
|
817 |
(atac 1) |
|
818 |
]); |
|
819 |
||
820 |
(* ----------------------------------------------------------------------- *) |
|
821 |
(* alternative prove for admissibility of ~stream_finite *) |
|
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
948
diff
changeset
|
822 |
(* show that stream_finite(s) = (? n. iterate n stl s = UU) *) |
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
948
diff
changeset
|
823 |
(* and prove adm. of ~(? n. iterate n stl s = UU) *) |
297 | 824 |
(* proof uses theorems stream_take_lemma5-7; stream_finite_lemma8 *) |
825 |
(* ----------------------------------------------------------------------- *) |
|
826 |
||
827 |
||
892 | 828 |
qed_goal "adm_not_stream_finite" Stream.thy "adm(%s. ~ stream_finite(s))" |
297 | 829 |
(fn prems => |
830 |
[ |
|
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
948
diff
changeset
|
831 |
(subgoal_tac "(!s.(~stream_finite(s))=(!n.iterate n stl s ~=UU))" 1), |
297 | 832 |
(etac (adm_cong RS iffD2)1), |
833 |
(REPEAT(resolve_tac adm_thms 1)), |
|
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
948
diff
changeset
|
834 |
(rtac cont_iterate2 1), |
297 | 835 |
(rtac allI 1), |
836 |
(rtac (stream_finite_lemma8 RS ssubst) 1), |
|
837 |
(fast_tac HOL_cs 1) |
|
838 |
]); |
|
839 |
||
840 |