| author | nipkow |
| Tue, 17 Oct 2000 08:00:46 +0200 | |
| changeset 10228 | e653cb933293 |
| parent 243 | c22b85994e17 |
| permissions | -rw-r--r-- |
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(* Title: HOLCF/cprod1.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 cprod1.thy |
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*) |
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open Cprod1; |
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val less_cprod1b = prove_goalw Cprod1.thy [less_cprod_def] |
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"less_cprod(p1,p2) = ( fst(p1) << fst(p2) & snd(p1) << snd(p2))" |
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(fn prems => |
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[ |
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(rtac refl 1) |
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]); |
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val less_cprod2a = prove_goalw Cprod1.thy [less_cprod_def] |
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"less_cprod(<x,y>,<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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(etac conjE 1), |
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(dtac (fst_conv RS subst) 1), |
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(dtac (fst_conv RS subst) 1), |
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(dtac (fst_conv RS subst) 1), |
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(dtac (snd_conv RS subst) 1), |
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(dtac (snd_conv RS subst) 1), |
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(dtac (snd_conv RS subst) 1), |
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(rtac conjI 1), |
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(etac UU_I 1), |
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(etac UU_I 1) |
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]); |
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val less_cprod2b = prove_goal Cprod1.thy |
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"less_cprod(p,<UU,UU>) ==> p=<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")] PairE 1),
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(hyp_subst_tac 1), |
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(dtac less_cprod2a 1), |
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(asm_simp_tac HOL_ss 1) |
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]); |
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val less_cprod2c = prove_goalw Cprod1.thy [less_cprod_def] |
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"less_cprod(<x1,y1>,<x2,y2>) ==> x1 << x2 & y1 << y2" |
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(fn prems => |
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[ |
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(cut_facts_tac prems 1), |
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(etac conjE 1), |
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(dtac (fst_conv RS subst) 1), |
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(dtac (fst_conv RS subst) 1), |
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(dtac (fst_conv RS subst) 1), |
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(dtac (snd_conv RS subst) 1), |
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(dtac (snd_conv RS subst) 1), |
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(dtac (snd_conv RS subst) 1), |
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(rtac conjI 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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(* less_cprod is a partial order on 'a * 'b *) |
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(* ------------------------------------------------------------------------ *) |
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val refl_less_cprod = prove_goalw Cprod1.thy [less_cprod_def] "less_cprod(p,p)" |
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(fn prems => |
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[ |
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(res_inst_tac [("p","p")] PairE 1),
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(hyp_subst_tac 1), |
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(simp_tac pair_ss 1), |
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(simp_tac Cfun_ss 1) |
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]); |
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val antisym_less_cprod = prove_goal Cprod1.thy |
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"[|less_cprod(p1,p2);less_cprod(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")] PairE 1),
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(hyp_subst_tac 1), |
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(res_inst_tac [("p","p2")] PairE 1),
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(hyp_subst_tac 1), |
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(dtac less_cprod2c 1), |
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(dtac less_cprod2c 1), |
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(etac conjE 1), |
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(etac conjE 1), |
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(rtac (Pair_eq RS ssubst) 1), |
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(fast_tac (HOL_cs addSIs [antisym_less]) 1) |
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]); |
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val trans_less_cprod = prove_goal Cprod1.thy |
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"[|less_cprod(p1,p2);less_cprod(p2,p3)|] ==> less_cprod(p1,p3)" |
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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")] PairE 1),
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(hyp_subst_tac 1), |
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(res_inst_tac [("p","p3")] PairE 1),
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(hyp_subst_tac 1), |
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(res_inst_tac [("p","p2")] PairE 1),
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(hyp_subst_tac 1), |
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(dtac less_cprod2c 1), |
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(dtac less_cprod2c 1), |
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(rtac (less_cprod1b RS ssubst) 1), |
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(simp_tac pair_ss 1), |
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(etac conjE 1), |
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(etac conjE 1), |
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(rtac conjI 1), |
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(etac trans_less 1), |
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(atac 1), |
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(etac trans_less 1), |
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(atac 1) |
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]); |
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