diff -r 2c38796b33b9 -r ee4dfce170a0 src/HOLCF/Sprod1.ML --- a/src/HOLCF/Sprod1.ML Sat Feb 15 18:24:05 1997 +0100 +++ b/src/HOLCF/Sprod1.ML Mon Feb 17 10:57:11 1997 +0100 @@ -1,183 +1,36 @@ -(* Title: HOLCF/sprod1.ML +(* Title: HOLCF/Sprod1.ML ID: $Id$ Author: Franz Regensburger Copyright 1993 Technische Universitaet Muenchen -Lemmas for theory sprod1.thy +Lemmas for theory Sprod1.thy *) open Sprod1; (* ------------------------------------------------------------------------ *) -(* reduction properties for less_sprod *) -(* ------------------------------------------------------------------------ *) - - -qed_goalw "less_sprod1a" Sprod1.thy [less_sprod_def] - "p1=Ispair UU UU ==> less_sprod p1 p2" - (fn prems => - [ - (cut_facts_tac prems 1), - (asm_simp_tac HOL_ss 1) - ]); - -qed_goalw "less_sprod1b" Sprod1.thy [less_sprod_def] - "p1~=Ispair UU UU ==> \ -\ less_sprod p1 p2 = ( Isfst p1 << Isfst p2 & Issnd p1 << Issnd p2)" - (fn prems => - [ - (cut_facts_tac prems 1), - (asm_simp_tac HOL_ss 1) - ]); - -qed_goal "less_sprod2a" Sprod1.thy - "less_sprod(Ispair x y)(Ispair UU UU) ==> x = UU | y = UU" -(fn prems => - [ - (cut_facts_tac prems 1), - (rtac (excluded_middle RS disjE) 1), - (atac 2), - (rtac disjI1 1), - (rtac antisym_less 1), - (rtac minimal 2), - (res_inst_tac [("s","Isfst(Ispair x y)"),("t","x")] subst 1), - (rtac Isfst 1), - (fast_tac HOL_cs 1), - (fast_tac HOL_cs 1), - (res_inst_tac [("s","Isfst(Ispair UU UU)"),("t","UU")] subst 1), - (simp_tac Sprod0_ss 1), - (rtac (defined_Ispair RS less_sprod1b RS iffD1 RS conjunct1) 1), - (REPEAT (fast_tac HOL_cs 1)) - ]); - -qed_goal "less_sprod2b" Sprod1.thy - "less_sprod p (Ispair UU UU) ==> p = Ispair UU UU" -(fn prems => - [ - (cut_facts_tac prems 1), - (res_inst_tac [("p","p")] IsprodE 1), - (atac 1), - (hyp_subst_tac 1), - (rtac strict_Ispair 1), - (etac less_sprod2a 1) - ]); - -qed_goal "less_sprod2c" Sprod1.thy - "[|less_sprod(Ispair xa ya)(Ispair x y);\ -\ xa ~= UU ; ya ~= UU; x ~= UU ; y ~= UU |] ==> xa << x & ya << y" -(fn prems => - [ - (rtac conjI 1), - (res_inst_tac [("s","Isfst(Ispair xa ya)"),("t","xa")] subst 1), - (simp_tac (Sprod0_ss addsimps prems)1), - (res_inst_tac [("s","Isfst(Ispair x y)"),("t","x")] subst 1), - (simp_tac (Sprod0_ss addsimps prems)1), - (rtac (defined_Ispair RS less_sprod1b RS iffD1 RS conjunct1) 1), - (resolve_tac prems 1), - (resolve_tac prems 1), - (simp_tac (Sprod0_ss addsimps prems)1), - (res_inst_tac [("s","Issnd(Ispair xa ya)"),("t","ya")] subst 1), - (simp_tac (Sprod0_ss addsimps prems)1), - (res_inst_tac [("s","Issnd(Ispair x y)"),("t","y")] subst 1), - (simp_tac (Sprod0_ss addsimps prems)1), - (rtac (defined_Ispair RS less_sprod1b RS iffD1 RS conjunct2) 1), - (resolve_tac prems 1), - (resolve_tac prems 1), - (simp_tac (Sprod0_ss addsimps prems)1) - ]); - -(* ------------------------------------------------------------------------ *) (* less_sprod is a partial order on Sprod *) (* ------------------------------------------------------------------------ *) -qed_goal "refl_less_sprod" Sprod1.thy "less_sprod p p" -(fn prems => - [ - (res_inst_tac [("p","p")] IsprodE 1), - (etac less_sprod1a 1), - (hyp_subst_tac 1), - (stac less_sprod1b 1), - (rtac defined_Ispair 1), - (REPEAT (fast_tac (HOL_cs addIs [refl_less]) 1)) - ]); - +qed_goalw "refl_less_sprod" thy [less_sprod_def]"less (p::'a ** 'b) p" +(fn prems => [(fast_tac (HOL_cs addIs [refl_less]) 1)]); -qed_goal "antisym_less_sprod" Sprod1.thy - "[|less_sprod p1 p2;less_sprod p2 p1|] ==> p1=p2" - (fn prems => - [ - (cut_facts_tac prems 1), - (res_inst_tac [("p","p1")] IsprodE 1), - (hyp_subst_tac 1), - (res_inst_tac [("p","p2")] IsprodE 1), - (hyp_subst_tac 1), - (rtac refl 1), - (hyp_subst_tac 1), - (rtac (strict_Ispair RS sym) 1), - (etac less_sprod2a 1), - (hyp_subst_tac 1), - (res_inst_tac [("p","p2")] IsprodE 1), - (hyp_subst_tac 1), - (rtac (strict_Ispair) 1), - (etac less_sprod2a 1), - (hyp_subst_tac 1), - (res_inst_tac [("x1","x"),("y1","xa"),("x","y"),("y","ya")] (arg_cong RS cong) 1), - (rtac antisym_less 1), - (asm_simp_tac (HOL_ss addsimps [less_sprod2c RS conjunct1]) 1), - (asm_simp_tac (HOL_ss addsimps [less_sprod2c RS conjunct1]) 1), - (rtac antisym_less 1), - (asm_simp_tac (HOL_ss addsimps [less_sprod2c RS conjunct2]) 1), - (asm_simp_tac (HOL_ss addsimps [less_sprod2c RS conjunct2]) 1) - ]); - -qed_goal "trans_less_sprod" Sprod1.thy - "[|less_sprod (p1::'a**'b) p2;less_sprod p2 p3|] ==> less_sprod p1 p3" - (fn prems => +qed_goalw "antisym_less_sprod" thy [less_sprod_def] + "[|less (p1::'a ** 'b) p2;less p2 p1|] ==> p1=p2" +(fn prems => [ (cut_facts_tac prems 1), - (res_inst_tac [("p","p1")] IsprodE 1), - (etac less_sprod1a 1), - (hyp_subst_tac 1), - (res_inst_tac [("p","p3")] IsprodE 1), - (hyp_subst_tac 1), - (res_inst_tac [("s","p2"),("t","Ispair (UU::'a)(UU::'b)")] subst 1), - (etac less_sprod2b 1), - (atac 1), - (hyp_subst_tac 1), - (res_inst_tac [("Q","p2=Ispair(UU::'a)(UU::'b)")] - (excluded_middle RS disjE) 1), - (stac (defined_Ispair RS less_sprod1b) 1), - (REPEAT (atac 1)), - (rtac conjI 1), - (res_inst_tac [("y","Isfst(p2)")] trans_less 1), - (rtac conjunct1 1), - (rtac (less_sprod1b RS subst) 1), - (rtac defined_Ispair 1), - (REPEAT (atac 1)), - (rtac conjunct1 1), - (rtac (less_sprod1b RS subst) 1), - (REPEAT (atac 1)), - (res_inst_tac [("y","Issnd(p2)")] trans_less 1), - (rtac conjunct2 1), - (rtac (less_sprod1b RS subst) 1), - (rtac defined_Ispair 1), - (REPEAT (atac 1)), - (rtac conjunct2 1), - (rtac (less_sprod1b RS subst) 1), - (REPEAT (atac 1)), - (hyp_subst_tac 1), - (res_inst_tac [("s","Ispair(UU::'a)(UU::'b)"),("t","Ispair x y")] - subst 1), - (etac (less_sprod2b RS sym) 1), - (atac 1) + (rtac Sel_injective_Sprod 1), + (fast_tac (HOL_cs addIs [antisym_less]) 1), + (fast_tac (HOL_cs addIs [antisym_less]) 1) ]); - - - - - - - - - +qed_goalw "trans_less_sprod" thy [less_sprod_def] + "[|less (p1::'a**'b) p2;less p2 p3|] ==> less p1 p3" +(fn prems => + [ + (cut_facts_tac prems 1), + (rtac conjI 1), + (fast_tac (HOL_cs addIs [trans_less]) 1), + (fast_tac (HOL_cs addIs [trans_less]) 1) + ]);