author | paulson |
Wed, 21 Aug 1996 13:22:23 +0200 | |
changeset 1933 | 8b24773de6db |
parent 1461 | 6bcb44e4d6e5 |
child 2033 | 639de962ded4 |
permissions | -rw-r--r-- |
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(* Title: HOLCF/sprod1.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 theory sprod1.thy |
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*) |
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open Sprod1; |
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(* ------------------------------------------------------------------------ *) |
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(* reduction properties for less_sprod *) |
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(* ------------------------------------------------------------------------ *) |
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qed_goalw "less_sprod1a" Sprod1.thy [less_sprod_def] |
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"p1=Ispair UU UU ==> less_sprod p1 p2" |
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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 HOL_ss 1) |
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]); |
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qed_goalw "less_sprod1b" Sprod1.thy [less_sprod_def] |
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"p1~=Ispair UU UU ==> \ |
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\ less_sprod p1 p2 = ( Isfst p1 << Isfst p2 & Issnd p1 << Issnd p2)" |
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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 HOL_ss 1) |
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]); |
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qed_goal "less_sprod2a" Sprod1.thy |
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"less_sprod(Ispair x y)(Ispair UU UU) ==> x = UU | y = UU" |
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(fn prems => |
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[ |
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(cut_facts_tac prems 1), |
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(rtac (excluded_middle RS disjE) 1), |
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(atac 2), |
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(rtac disjI1 1), |
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(rtac antisym_less 1), |
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(rtac minimal 2), |
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(res_inst_tac [("s","Isfst(Ispair x y)"),("t","x")] subst 1), |
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(rtac Isfst 1), |
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(fast_tac HOL_cs 1), |
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(fast_tac HOL_cs 1), |
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(res_inst_tac [("s","Isfst(Ispair UU UU)"),("t","UU")] subst 1), |
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(simp_tac Sprod0_ss 1), |
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(rtac (defined_Ispair RS less_sprod1b RS iffD1 RS conjunct1) 1), |
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(REPEAT (fast_tac HOL_cs 1)) |
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]); |
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qed_goal "less_sprod2b" Sprod1.thy |
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"less_sprod p (Ispair UU UU) ==> p = Ispair UU UU" |
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(fn prems => |
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[ |
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(cut_facts_tac prems 1), |
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(res_inst_tac [("p","p")] IsprodE 1), |
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(atac 1), |
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(hyp_subst_tac 1), |
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(rtac strict_Ispair 1), |
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(etac less_sprod2a 1) |
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]); |
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qed_goal "less_sprod2c" Sprod1.thy |
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"[|less_sprod(Ispair xa ya)(Ispair x y);\ |
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\ xa ~= UU ; ya ~= UU; x ~= UU ; y ~= UU |] ==> xa << x & ya << y" |
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(fn prems => |
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[ |
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(rtac conjI 1), |
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(res_inst_tac [("s","Isfst(Ispair xa ya)"),("t","xa")] subst 1), |
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(simp_tac (Sprod0_ss addsimps prems)1), |
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(res_inst_tac [("s","Isfst(Ispair x y)"),("t","x")] subst 1), |
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(simp_tac (Sprod0_ss addsimps prems)1), |
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(rtac (defined_Ispair RS less_sprod1b RS iffD1 RS conjunct1) 1), |
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(resolve_tac prems 1), |
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(resolve_tac prems 1), |
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(simp_tac (Sprod0_ss addsimps prems)1), |
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(res_inst_tac [("s","Issnd(Ispair xa ya)"),("t","ya")] subst 1), |
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(simp_tac (Sprod0_ss addsimps prems)1), |
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(res_inst_tac [("s","Issnd(Ispair x y)"),("t","y")] subst 1), |
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(simp_tac (Sprod0_ss addsimps prems)1), |
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(rtac (defined_Ispair RS less_sprod1b RS iffD1 RS conjunct2) 1), |
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(resolve_tac prems 1), |
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(resolve_tac prems 1), |
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(simp_tac (Sprod0_ss addsimps prems)1) |
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]); |
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(* ------------------------------------------------------------------------ *) |
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(* less_sprod is a partial order on Sprod *) |
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(* ------------------------------------------------------------------------ *) |
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qed_goal "refl_less_sprod" Sprod1.thy "less_sprod p p" |
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(fn prems => |
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(res_inst_tac [("p","p")] IsprodE 1), |
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(etac less_sprod1a 1), |
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(hyp_subst_tac 1), |
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(rtac (less_sprod1b RS ssubst) 1), |
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(rtac defined_Ispair 1), |
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(REPEAT (fast_tac (HOL_cs addIs [refl_less]) 1)) |
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]); |
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qed_goal "antisym_less_sprod" Sprod1.thy |
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"[|less_sprod p1 p2;less_sprod p2 p1|] ==> p1=p2" |
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(fn prems => |
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[ |
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(cut_facts_tac prems 1), |
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(res_inst_tac [("p","p1")] IsprodE 1), |
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(hyp_subst_tac 1), |
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(res_inst_tac [("p","p2")] IsprodE 1), |
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(hyp_subst_tac 1), |
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(rtac refl 1), |
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(hyp_subst_tac 1), |
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(rtac (strict_Ispair RS sym) 1), |
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(etac less_sprod2a 1), |
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(hyp_subst_tac 1), |
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(res_inst_tac [("p","p2")] IsprodE 1), |
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(hyp_subst_tac 1), |
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(rtac (strict_Ispair) 1), |
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(etac less_sprod2a 1), |
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(hyp_subst_tac 1), |
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(res_inst_tac [("x1","x"),("y1","xa"),("x","y"),("y","ya")] (arg_cong RS cong) 1), |
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(rtac antisym_less 1), |
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(asm_simp_tac (HOL_ss addsimps [less_sprod2c RS conjunct1]) 1), |
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(asm_simp_tac (HOL_ss addsimps [less_sprod2c RS conjunct1]) 1), |
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(rtac antisym_less 1), |
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(asm_simp_tac (HOL_ss addsimps [less_sprod2c RS conjunct2]) 1), |
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(asm_simp_tac (HOL_ss addsimps [less_sprod2c RS conjunct2]) 1) |
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]); |
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qed_goal "trans_less_sprod" Sprod1.thy |
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"[|less_sprod (p1::'a**'b) p2;less_sprod p2 p3|] ==> less_sprod p1 p3" |
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(fn prems => |
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(cut_facts_tac prems 1), |
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(res_inst_tac [("p","p1")] IsprodE 1), |
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(etac less_sprod1a 1), |
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(hyp_subst_tac 1), |
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(res_inst_tac [("p","p3")] IsprodE 1), |
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(hyp_subst_tac 1), |
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(res_inst_tac [("s","p2"),("t","Ispair (UU::'a)(UU::'b)")] subst 1), |
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(etac less_sprod2b 1), |
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(atac 1), |
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(hyp_subst_tac 1), |
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(res_inst_tac [("Q","p2=Ispair(UU::'a)(UU::'b)")] |
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(excluded_middle RS disjE) 1), |
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(rtac (defined_Ispair RS less_sprod1b RS ssubst) 1), |
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(REPEAT (atac 1)), |
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(rtac conjI 1), |
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(res_inst_tac [("y","Isfst(p2)")] trans_less 1), |
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(rtac conjunct1 1), |
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(rtac (less_sprod1b RS subst) 1), |
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(rtac defined_Ispair 1), |
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(REPEAT (atac 1)), |
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(rtac conjunct1 1), |
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(rtac (less_sprod1b RS subst) 1), |
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(REPEAT (atac 1)), |
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(res_inst_tac [("y","Issnd(p2)")] trans_less 1), |
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(rtac conjunct2 1), |
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(rtac (less_sprod1b RS subst) 1), |
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(rtac defined_Ispair 1), |
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(REPEAT (atac 1)), |
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(rtac conjunct2 1), |
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(rtac (less_sprod1b RS subst) 1), |
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(REPEAT (atac 1)), |
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(hyp_subst_tac 1), |
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(res_inst_tac [("s","Ispair(UU::'a)(UU::'b)"),("t","Ispair x y")] |
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subst 1), |
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(etac (less_sprod2b RS sym) 1), |
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(atac 1) |
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]); |
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