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(* Title: FOL/FOL.ML

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ID: $Id$

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Author: Lawrence C Paulson, Cambridge University Computer Laboratory

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Copyright 1991 University of Cambridge


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Tactics and lemmas for FOL.thy (classical FirstOrder Logic)

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*)


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open FOL;


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(*** Classical introduction rules for  and EX ***)


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qed_goal "disjCI" FOL.thy

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"(~Q ==> P) ==> PQ"


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(fn prems=>

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[ (rtac classical 1),

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(REPEAT (ares_tac (prems@[disjI1,notI]) 1)),


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(REPEAT (ares_tac (prems@[disjI2,notE]) 1)) ]);


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(*introduction rule involving only EX*)

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qed_goal "ex_classical" FOL.thy

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"( ~(EX x. P(x)) ==> P(a)) ==> EX x.P(x)"


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(fn prems=>

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[ (rtac classical 1),

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(eresolve_tac (prems RL [exI]) 1) ]);


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(*version of above, simplifying ~EX to ALL~ *)

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qed_goal "exCI" FOL.thy

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"(ALL x. ~P(x) ==> P(a)) ==> EX x.P(x)"


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(fn [prem]=>

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[ (rtac ex_classical 1),

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(resolve_tac [notI RS allI RS prem] 1),

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(etac notE 1),


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(etac exI 1) ]);

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qed_goal "excluded_middle" FOL.thy "~P  P"

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(fn _=> [ rtac disjCI 1, assume_tac 1 ]);


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(*For disjunctive case analysis*)


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fun excluded_middle_tac sP =


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res_inst_tac [("Q",sP)] (excluded_middle RS disjE);

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(*** Special elimination rules *)


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(*Classical implies (>) elimination. *)

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qed_goal "impCE" FOL.thy

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"[ P>Q; ~P ==> R; Q ==> R ] ==> R"


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(fn major::prems=>


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[ (resolve_tac [excluded_middle RS disjE] 1),


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(DEPTH_SOLVE (ares_tac (prems@[major RS mp]) 1)) ]);


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(*Double negation law*)

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qed_goal "notnotD" FOL.thy "~~P ==> P"

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(fn [major]=>

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[ (rtac classical 1), (eresolve_tac [major RS notE] 1) ]);

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(*** Tactics for implication and contradiction ***)


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(*Classical <> elimination. Proof substitutes P=Q in


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~P ==> ~Q and P ==> Q *)

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qed_goalw "iffCE" FOL.thy [iff_def]

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"[ P<>Q; [ P; Q ] ==> R; [ ~P; ~Q ] ==> R ] ==> R"


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(fn prems =>

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[ (rtac conjE 1),

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(REPEAT (DEPTH_SOLVE_1

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(etac impCE 1 ORELSE mp_tac 1 ORELSE ares_tac prems 1))) ]);
