src/HOL/HOL_lemmas.ML
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(*  Title:      HOL/HOL_lemmas.ML
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    ID:         $Id$
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    Author:     Tobias Nipkow
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    Copyright   1991  University of Cambridge
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Derived rules from Appendix of Mike Gordons HOL Report, Cambridge TR 68.
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*)
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(* ML bindings *)
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val plusI = thm "plusI";
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val minusI = thm "minusI";
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val timesI = thm "timesI";
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val powerI = thm "powerI";
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val eq_reflection = thm "eq_reflection";
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val refl = thm "refl";
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val subst = thm "subst";
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val ext = thm "ext";
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val selectI = thm "selectI";
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val impI = thm "impI";
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val mp = thm "mp";
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val True_def = thm "True_def";
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val All_def = thm "All_def";
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val Ex_def = thm "Ex_def";
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val False_def = thm "False_def";
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val not_def = thm "not_def";
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val and_def = thm "and_def";
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val or_def = thm "or_def";
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val Ex1_def = thm "Ex1_def";
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val iff = thm "iff";
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val True_or_False = thm "True_or_False";
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val Let_def = thm "Let_def";
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val if_def = thm "if_def";
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val arbitrary_def = thm "arbitrary_def";
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(** Equality **)
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section "=";
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Goal "s=t ==> t=s";
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by (etac subst 1);
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by (rtac refl 1);
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qed "sym";
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(*calling "standard" reduces maxidx to 0*)
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bind_thm ("ssubst", sym RS subst);
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Goal "[| r=s; s=t |] ==> r=t";
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by (etac subst 1 THEN assume_tac 1);
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qed "trans";
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val prems = goal (the_context ()) "(A == B) ==> A = B";
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by (rewrite_goals_tac prems);
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by (rtac refl 1);
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qed "def_imp_eq";
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(*Useful with eresolve_tac for proving equalties from known equalities.
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        a = b
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        |   |
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        c = d   *)
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Goal "[| a=b;  a=c;  b=d |] ==> c=d";
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by (rtac trans 1);
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by (rtac trans 1);
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by (rtac sym 1);
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by (REPEAT (assume_tac 1)) ;
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qed "box_equals";
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(** Congruence rules for meta-application **)
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section "Congruence";
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(*similar to AP_THM in Gordon's HOL*)
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Goal "(f::'a=>'b) = g ==> f(x)=g(x)";
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by (etac subst 1);
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by (rtac refl 1);
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qed "fun_cong";
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(*similar to AP_TERM in Gordon's HOL and FOL's subst_context*)
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Goal "x=y ==> f(x)=f(y)";
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by (etac subst 1);
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by (rtac refl 1);
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qed "arg_cong";
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Goal "[| f = g; (x::'a) = y |] ==> f(x) = g(y)";
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by (etac subst 1);
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by (etac subst 1);
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by (rtac refl 1);
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qed "cong";
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(** Equality of booleans -- iff **)
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section "iff";
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val prems = Goal "[| P ==> Q;  Q ==> P |] ==> P=Q";
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by (REPEAT (ares_tac (prems@[impI, iff RS mp RS mp]) 1));
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qed "iffI";
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Goal "[| P=Q; Q |] ==> P";
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by (etac ssubst 1);
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by (assume_tac 1);
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qed "iffD2";
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Goal "[| Q; P=Q |] ==> P";
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by (etac iffD2 1);
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by (assume_tac 1);
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qed "rev_iffD2";
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bind_thm ("iffD1", sym RS iffD2);
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bind_thm ("rev_iffD1", sym RSN (2, rev_iffD2));
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val [p1,p2] = Goal "[| P=Q; [| P --> Q; Q --> P |] ==> R |] ==> R";
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by (REPEAT (ares_tac [p1 RS iffD2, p1 RS iffD1, p2, impI] 1));
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qed "iffE";
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(** True **)
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section "True";
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Goalw [True_def] "True";
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by (rtac refl 1);
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qed "TrueI";
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Goal "P ==> P=True";
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by (REPEAT (ares_tac [iffI,TrueI] 1));
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qed "eqTrueI";
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Goal "P=True ==> P";
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by (etac iffD2 1);
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by (rtac TrueI 1);
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qed "eqTrueE";
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(** Universal quantifier **)
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section "!";
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val prems = Goalw [All_def] "(!!x::'a. P(x)) ==> ! x. P(x)";
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by (resolve_tac (prems RL [eqTrueI RS ext]) 1);
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qed "allI";
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Goalw [All_def] "! x::'a. P(x) ==> P(x)";
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by (rtac eqTrueE 1);
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by (etac fun_cong 1);
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qed "spec";
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val major::prems= goal (the_context ()) "[| ! x. P(x);  P(x) ==> R |] ==> R";
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by (REPEAT (resolve_tac (prems @ [major RS spec]) 1)) ;
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qed "allE";
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val prems = goal (the_context ()) 
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    "[| ! x. P(x);  [| P(x); ! x. P(x) |] ==> R |] ==> R";
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by (REPEAT (resolve_tac (prems @ (prems RL [spec])) 1)) ;
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qed "all_dupE";
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(** False ** Depends upon spec; it is impossible to do propositional logic
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             before quantifiers! **)
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section "False";
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Goalw [False_def] "False ==> P";
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by (etac spec 1);
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qed "FalseE";
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Goal "False=True ==> P";
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by (etac (eqTrueE RS FalseE) 1);
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qed "False_neq_True";
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(** Negation **)
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section "~";
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val prems = Goalw [not_def] "(P ==> False) ==> ~P";
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by (rtac impI 1);
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by (eresolve_tac prems 1);
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qed "notI";
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Goal "False ~= True";
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by (rtac notI 1);
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by (etac False_neq_True 1);
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qed "False_not_True";
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Goal "True ~= False";
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by (rtac notI 1);
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by (dtac sym 1);
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by (etac False_neq_True 1);
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qed "True_not_False";
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Goalw [not_def] "[| ~P;  P |] ==> R";
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by (etac (mp RS FalseE) 1);
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by (assume_tac 1);
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qed "notE";
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bind_thm ("classical2", notE RS notI);
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Goal "[| P; ~P |] ==> R";
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by (etac notE 1);
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by (assume_tac 1);
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qed "rev_notE";
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(** Implication **)
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section "-->";
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val prems = Goal "[| P-->Q;  P;  Q ==> R |] ==> R";
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by (REPEAT (resolve_tac (prems@[mp]) 1));
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qed "impE";
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(* Reduces Q to P-->Q, allowing substitution in P. *)
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Goal "[| P;  P --> Q |] ==> Q";
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by (REPEAT (ares_tac [mp] 1)) ;
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qed "rev_mp";
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val [major,minor] = Goal "[| ~Q;  P==>Q |] ==> ~P";
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by (rtac (major RS notE RS notI) 1);
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by (etac minor 1) ;
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qed "contrapos";
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val [major,minor] = Goal "[| P==>Q; ~Q |] ==> ~P";
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by (rtac (minor RS contrapos) 1);
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by (etac major 1) ;
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qed "rev_contrapos";
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(* ~(?t = ?s) ==> ~(?s = ?t) *)
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bind_thm("not_sym", sym COMP rev_contrapos);
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(** Existential quantifier **)
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section "?";
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Goalw [Ex_def] "P x ==> ? x::'a. P x";
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by (etac selectI 1) ;
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qed "exI";
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val [major,minor] = 
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Goalw [Ex_def] "[| ? x::'a. P(x); !!x. P(x) ==> Q |] ==> Q";
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by (rtac (major RS minor) 1);
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qed "exE";
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(** Conjunction **)
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section "&";
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Goalw [and_def] "[| P; Q |] ==> P&Q";
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by (rtac (impI RS allI) 1);
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by (etac (mp RS mp) 1);
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by (REPEAT (assume_tac 1));
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qed "conjI";
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Goalw [and_def] "[| P & Q |] ==> P";
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by (dtac spec 1) ;
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by (etac mp 1);
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by (REPEAT (ares_tac [impI] 1));
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qed "conjunct1";
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Goalw [and_def] "[| P & Q |] ==> Q";
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by (dtac spec 1) ;
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by (etac mp 1);
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by (REPEAT (ares_tac [impI] 1));
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qed "conjunct2";
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val [major,minor] =
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Goal "[| P&Q;  [| P; Q |] ==> R |] ==> R";
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by (rtac minor 1);
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by (rtac (major RS conjunct1) 1);
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by (rtac (major RS conjunct2) 1);
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qed "conjE";
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val prems =
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Goal "[| P; P ==> Q |] ==> P & Q";
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by (REPEAT (resolve_tac (conjI::prems) 1));
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qed "context_conjI";
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(** Disjunction *)
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section "|";
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Goalw [or_def] "P ==> P|Q";
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by (REPEAT (resolve_tac [allI,impI] 1));
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by (etac mp 1 THEN assume_tac 1);
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qed "disjI1";
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Goalw [or_def] "Q ==> P|Q";
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by (REPEAT (resolve_tac [allI,impI] 1));
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by (etac mp 1 THEN assume_tac 1);
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qed "disjI2";
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val [major,minorP,minorQ] =
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Goalw [or_def]  "[| P | Q; P ==> R; Q ==> R |] ==> R";
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by (rtac (major RS spec RS mp RS mp) 1);
paulson
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by (DEPTH_SOLVE (ares_tac [impI,minorP,minorQ] 1));
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qed "disjE";
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(** CCONTR -- classical logic **)
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section "classical logic";
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val [prem] = Goal  "(~P ==> P) ==> P";
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by (rtac (True_or_False RS disjE RS eqTrueE) 1);
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   296
by (assume_tac 1);
paulson
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   297
by (rtac (notI RS prem RS eqTrueI) 1);
paulson
parents: 8276
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   298
by (etac subst 1);
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by (assume_tac 1);
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qed "classical";
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7832
77bac5d84162 bind_thm "ccontr";
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bind_thm ("ccontr", FalseE RS classical);
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(*Double negation law*)
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Goal "~~P ==> P";
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by (rtac classical 1);
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by (etac notE 1);
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by (assume_tac 1);
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qed "notnotD";
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   310
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val [p1,p2] = Goal "[| Q; ~ P ==> ~ Q |] ==> P";
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by (rtac classical 1);
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by (dtac p2 1);
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   314
by (etac notE 1);
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   315
by (rtac p1 1);
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qed "contrapos2";
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   317
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val [p1,p2] = Goal "[| P;  Q ==> ~ P |] ==> ~ Q";
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   319
by (rtac notI 1);
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diff changeset
   320
by (dtac p2 1);
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   321
by (etac notE 1);
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   322
by (rtac p1 1);
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   323
qed "swap2";
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   324
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(** Unique existence **)
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section "?!";
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   327
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val prems = Goalw [Ex1_def] "[| P(a);  !!x. P(x) ==> x=a |] ==> ?! x. P(x)";
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by (REPEAT (ares_tac (prems@[exI,conjI,allI,impI]) 1));
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qed "ex1I";
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(*Sometimes easier to use: the premises have no shared variables.  Safe!*)
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val [ex_prem,eq] = Goal
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    "[| ? x. P(x);  !!x y. [| P(x); P(y) |] ==> x=y |] ==> ?! x. P(x)";
8529
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by (rtac (ex_prem RS exE) 1);
7357
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by (REPEAT (ares_tac [ex1I,eq] 1)) ;
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qed "ex_ex1I";
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   338
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val major::prems = Goalw [Ex1_def]
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   340
    "[| ?! x. P(x);  !!x. [| P(x);  ! y. P(y) --> y=x |] ==> R |] ==> R";
paulson
parents: 8276
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   341
by (rtac (major RS exE) 1);
paulson
parents: 8276
diff changeset
   342
by (REPEAT (etac conjE 1 ORELSE ares_tac prems 1));
paulson
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qed "ex1E";
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Goal "?! x. P x ==> ? x. P x";
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   346
by (etac ex1E 1);
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diff changeset
   347
by (rtac exI 1);
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diff changeset
   348
by (assume_tac 1);
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   349
qed "ex1_implies_ex";
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   350
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   351
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   352
(** Select: Hilbert's Epsilon-operator **)
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section "@";
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   355
(*Easier to apply than selectI: conclusion has only one occurrence of P*)
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   356
val prems = Goal
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   357
    "[| P a;  !!x. P x ==> Q x |] ==> Q (@x. P x)";
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diff changeset
   358
by (resolve_tac prems 1);
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parents:
diff changeset
   359
by (rtac selectI 1);
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diff changeset
   360
by (resolve_tac prems 1) ;
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wenzelm
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diff changeset
   361
qed "selectI2";
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diff changeset
   362
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   363
(*Easier to apply than selectI2 if witness ?a comes from an EX-formula*)
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   364
val [major,minor] = Goal "[| ? a. P a;  !!x. P x ==> Q x |] ==> Q (Eps P)";
paulson
parents: 8276
diff changeset
   365
by (rtac (major RS exE) 1);
paulson
parents: 8276
diff changeset
   366
by (etac selectI2 1 THEN etac minor 1);
paulson
parents: 8276
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   367
qed "selectI2EX";
7357
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diff changeset
   368
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   369
val prems = Goal
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   370
    "[| P a;  !!x. P x ==> x=a |] ==> (@x. P x) = a";
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diff changeset
   371
by (rtac selectI2 1);
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   372
by (REPEAT (ares_tac prems 1)) ;
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   373
qed "select_equality";
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   374
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   375
Goalw [Ex1_def] "[| ?!x. P x; P a |] ==> (@x. P x) = a";
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   376
by (rtac select_equality 1);
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   377
by (atac 1);
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   378
by (etac exE 1);
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   379
by (etac conjE 1);
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   380
by (rtac allE 1);
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   381
by (atac 1);
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   382
by (etac impE 1);
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   383
by (atac 1);
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   384
by (etac ssubst 1);
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   385
by (etac allE 1);
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   386
by (etac mp 1);
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   387
by (atac 1);
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   388
qed "select1_equality";
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   389
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   390
Goal "P (@ x. P x) =  (? x. P x)";
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   391
by (rtac iffI 1);
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   392
by (etac exI 1);
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   393
by (etac exE 1);
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   394
by (etac selectI 1);
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   395
qed "select_eq_Ex";
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   396
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   397
Goal "(@y. y=x) = x";
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   398
by (rtac select_equality 1);
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   399
by (rtac refl 1);
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   400
by (atac 1);
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   401
qed "Eps_eq";
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   402
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   403
Goal "(Eps (op = x)) = x";
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   404
by (rtac select_equality 1);
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   405
by (rtac refl 1);
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   406
by (etac sym 1);
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   407
qed "Eps_sym_eq";
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   408
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   409
(** Classical intro rules for disjunction and existential quantifiers *)
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   410
section "classical intro rules";
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   411
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   412
val prems= Goal "(~Q ==> P) ==> P|Q";
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   413
by (rtac classical 1);
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   414
by (REPEAT (ares_tac (prems@[disjI1,notI]) 1));
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   415
by (REPEAT (ares_tac (prems@[disjI2,notE]) 1)) ;
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   416
qed "disjCI";
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   417
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   418
Goal "~P | P";
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   419
by (REPEAT (ares_tac [disjCI] 1)) ;
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   420
qed "excluded_middle";
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   421
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   422
(*For disjunctive case analysis*)
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   423
fun excluded_middle_tac sP =
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   424
    res_inst_tac [("Q",sP)] (excluded_middle RS disjE);
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   425
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   426
(*Classical implies (-->) elimination. *)
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   427
val major::prems = Goal "[| P-->Q; ~P ==> R; Q ==> R |] ==> R";
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   428
by (rtac (excluded_middle RS disjE) 1);
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   429
by (REPEAT (DEPTH_SOLVE_1 (ares_tac (prems @ [major RS mp]) 1)));
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   430
qed "impCE";
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   431
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   432
(*This version of --> elimination works on Q before P.  It works best for
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   433
  those cases in which P holds "almost everywhere".  Can't install as
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   434
  default: would break old proofs.*)
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   435
val major::prems = Goal
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   436
    "[| P-->Q;  Q ==> R;  ~P ==> R |] ==> R";
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   437
by (resolve_tac [excluded_middle RS disjE] 1);
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   438
by (DEPTH_SOLVE (ares_tac (prems@[major RS mp]) 1)) ;
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   439
qed "impCE'";
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   440
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   441
(*Classical <-> elimination. *)
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   442
val major::prems = Goal
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   443
    "[| P=Q;  [| P; Q |] ==> R;  [| ~P; ~Q |] ==> R |] ==> R";
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   444
by (rtac (major RS iffE) 1);
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   445
by (REPEAT (DEPTH_SOLVE_1 
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   446
	    (eresolve_tac ([asm_rl,impCE,notE]@prems) 1)));
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   447
qed "iffCE";
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   448
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   449
val prems = Goal "(! x. ~P(x) ==> P(a)) ==> ? x. P(x)";
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   450
by (rtac ccontr 1);
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   451
by (REPEAT (ares_tac (prems@[exI,allI,notI,notE]) 1))  ;
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   452
qed "exCI";
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   453
8964
df06ec11bbfa some lemmas about plus_ac0
paulson
parents: 8529
diff changeset
   454
Goal "x + (y+z) = y + ((x+z)::'a::plus_ac0)";
df06ec11bbfa some lemmas about plus_ac0
paulson
parents: 8529
diff changeset
   455
by (rtac (thm"plus_ac0.commute" RS trans) 1);
df06ec11bbfa some lemmas about plus_ac0
paulson
parents: 8529
diff changeset
   456
by (rtac (thm"plus_ac0.assoc" RS trans) 1);
df06ec11bbfa some lemmas about plus_ac0
paulson
parents: 8529
diff changeset
   457
by (rtac (thm"plus_ac0.commute" RS arg_cong) 1);
df06ec11bbfa some lemmas about plus_ac0
paulson
parents: 8529
diff changeset
   458
qed "plus_ac0_left_commute";
df06ec11bbfa some lemmas about plus_ac0
paulson
parents: 8529
diff changeset
   459
df06ec11bbfa some lemmas about plus_ac0
paulson
parents: 8529
diff changeset
   460
Goal "x + 0 = (x ::'a::plus_ac0)";
df06ec11bbfa some lemmas about plus_ac0
paulson
parents: 8529
diff changeset
   461
by (rtac (thm"plus_ac0.commute" RS trans) 1);
df06ec11bbfa some lemmas about plus_ac0
paulson
parents: 8529
diff changeset
   462
by (rtac (thm"plus_ac0.zero") 1);
df06ec11bbfa some lemmas about plus_ac0
paulson
parents: 8529
diff changeset
   463
qed "plus_ac0_zero_right";
df06ec11bbfa some lemmas about plus_ac0
paulson
parents: 8529
diff changeset
   464
df06ec11bbfa some lemmas about plus_ac0
paulson
parents: 8529
diff changeset
   465
bind_thms ("plus_ac0", [thm"plus_ac0.assoc", thm"plus_ac0.commute", 
df06ec11bbfa some lemmas about plus_ac0
paulson
parents: 8529
diff changeset
   466
			plus_ac0_left_commute,
df06ec11bbfa some lemmas about plus_ac0
paulson
parents: 8529
diff changeset
   467
			thm"plus_ac0.zero", plus_ac0_zero_right]);
7357
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   468
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   469
(* case distinction *)
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   470
8529
paulson
parents: 8276
diff changeset
   471
val [prem1,prem2] = Goal "[| P ==> Q; ~P ==> Q |] ==> Q";
paulson
parents: 8276
diff changeset
   472
by (rtac (excluded_middle RS disjE) 1);
paulson
parents: 8276
diff changeset
   473
by (etac prem2 1);
paulson
parents: 8276
diff changeset
   474
by (etac prem1 1);
paulson
parents: 8276
diff changeset
   475
qed "case_split_thm";
7357
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   476
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   477
fun case_tac a = res_inst_tac [("P",a)] case_split_thm;
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   478
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   479
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   480
(** Standard abbreviations **)
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   481
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   482
(*Apply an equality or definition ONCE.
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   483
  Fails unless the substitution has an effect*)
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   484
fun stac th = 
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   485
  let val th' = th RS def_imp_eq handle THM _ => th
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   486
  in  CHANGED_GOAL (rtac (th' RS ssubst))
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   487
  end;
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   488
7490
9a74b57740d1 added smp_tac
oheimb
parents: 7427
diff changeset
   489
(* combination of (spec RS spec RS ...(j times) ... spec RS mp *) 
9a74b57740d1 added smp_tac
oheimb
parents: 7427
diff changeset
   490
local
9a74b57740d1 added smp_tac
oheimb
parents: 7427
diff changeset
   491
  fun wrong_prem (Const ("All", _) $ (Abs (_, _, t))) = wrong_prem t
9a74b57740d1 added smp_tac
oheimb
parents: 7427
diff changeset
   492
  |   wrong_prem (Bound _) = true
9a74b57740d1 added smp_tac
oheimb
parents: 7427
diff changeset
   493
  |   wrong_prem _ = false;
7533
1659dc4e3552 minor change to smp_tac
oheimb
parents: 7490
diff changeset
   494
  val filter_right = filter (fn t => not (wrong_prem (HOLogic.dest_Trueprop (hd (Thm.prems_of t)))));
7490
9a74b57740d1 added smp_tac
oheimb
parents: 7427
diff changeset
   495
in
9a74b57740d1 added smp_tac
oheimb
parents: 7427
diff changeset
   496
  fun smp i = funpow i (fn m => filter_right ([spec] RL m)) ([mp]);
9a74b57740d1 added smp_tac
oheimb
parents: 7427
diff changeset
   497
  fun smp_tac j = EVERY'[dresolve_tac (smp j), atac]
9a74b57740d1 added smp_tac
oheimb
parents: 7427
diff changeset
   498
end;
9a74b57740d1 added smp_tac
oheimb
parents: 7427
diff changeset
   499
9a74b57740d1 added smp_tac
oheimb
parents: 7427
diff changeset
   500
7357
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   501
fun strip_tac i = REPEAT(resolve_tac [impI,allI] i); 
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   502
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   503
(** strip ! and --> from proved goal while preserving !-bound var names **)
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   504
7884
2c65e8212115 qed_spec_mp is a mess;
wenzelm
parents: 7832
diff changeset
   505
(** THIS CODE IS A MESS!!! **)
2c65e8212115 qed_spec_mp is a mess;
wenzelm
parents: 7832
diff changeset
   506
7357
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   507
local
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   508
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   509
(* Use XXX to avoid forall_intr failing because of duplicate variable name *)
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   510
val myspec = read_instantiate [("P","?XXX")] spec;
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   511
val _ $ (_ $ (vx as Var(_,vxT))) = concl_of myspec;
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   512
val cvx = cterm_of (#sign(rep_thm myspec)) vx;
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   513
val aspec = forall_intr cvx myspec;
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   514
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   515
in
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   516
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   517
fun RSspec th =
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   518
  (case concl_of th of
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   519
     _ $ (Const("All",_) $ Abs(a,_,_)) =>
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   520
         let val ca = cterm_of (#sign(rep_thm th)) (Var((a,0),vxT))
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   521
         in th RS forall_elim ca aspec end
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   522
  | _ => raise THM("RSspec",0,[th]));
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   523
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   524
fun RSmp th =
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   525
  (case concl_of th of
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   526
     _ $ (Const("op -->",_)$_$_) => th RS mp
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   527
  | _ => raise THM("RSmp",0,[th]));
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   528
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   529
fun normalize_thm funs =
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   530
  let fun trans [] th = th
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   531
	| trans (f::fs) th = (trans funs (f th)) handle THM _ => trans fs th
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   532
  in zero_var_indexes o trans funs end;
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   533
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   534
fun qed_spec_mp name =
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   535
  let val thm = normalize_thm [RSspec,RSmp] (result())
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   536
  in ThmDatabase.ml_store_thm(name, thm) end;
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   537
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   538
fun qed_goal_spec_mp name thy s p = 
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   539
	bind_thm (name, normalize_thm [RSspec,RSmp] (prove_goal thy s p));
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   540
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   541
fun qed_goalw_spec_mp name thy defs s p = 
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   542
	bind_thm (name, normalize_thm [RSspec,RSmp] (prove_goalw thy defs s p));
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   543
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   544
end;
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   545
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   546
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   547
(* attributes *)
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   548
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   549
local
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   550
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   551
fun gen_rulify x =
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   552
  Attrib.no_args (Drule.rule_attribute (fn _ => (normalize_thm [RSspec, RSmp]))) x;
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   553
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   554
in
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   555
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   556
val attrib_setup =
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   557
 [Attrib.add_attributes
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   558
  [("rulify", (gen_rulify, gen_rulify), "put theorem into standard rule form")]];
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   559
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents:
diff changeset
   560
end;