author  wenzelm 
Mon, 16 Nov 1998 13:54:35 +0100  
changeset 5897  b3548f939dd2 
parent 5704  1ddf7e1e8b19 
child 7879  4547f0bd9454 
permissions  rwrr 
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split_paired_all.ML: turn surjective pairing into split rule;
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(* Title: Provers/split_paired_all.ML 
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ID: $Id$ 
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split_paired_all.ML: turn surjective pairing into split rule;
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Author: Markus Wenzel, TU Muenchen 
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Derived rule for turning metalevel surjective pairing into split rule: 
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p == (fst p, snd p) 
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!!a b. PROP (a, b) == !! x. PROP P x 
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*) 
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signature SPLIT_PAIRED_ALL = 
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sig 
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val rule: thm > thm 
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end; 
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structure SplitPairedAll: SPLIT_PAIRED_ALL = 
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struct 
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fun all x T t = Term.all T $ Abs (x, T, t); 
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infixr ==>; 
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val op ==> = Logic.mk_implies; 
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fun rule raw_surj_pair = 
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let 
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val ct = Thm.cterm_of (Thm.sign_of_thm raw_surj_pair); 
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5704  32 
val surj_pair = Drule.unvarify (standard raw_surj_pair); 
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val used = Term.add_term_names (#prop (Thm.rep_thm surj_pair), []); 
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val (p, con $ _ $ _) = Logic.dest_equals (#prop (rep_thm surj_pair)); 
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val pT as Type (_, [aT, bT]) = fastype_of p; 
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val P = Free (variant used "P", pT > propT); 
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5704  39 
(*"!!a b. PROP (a, b)"*) 
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val all_a_b = all "a" aT (all "b" bT (P $ (con $ Bound 1 $ Bound 0))); 

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(*"!!x. PROP P x"*) 

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val all_x = all "x" pT (P $ Bound 0); 

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5704  44 
(*lemma "P p == P (fst p, snd p)"*) 
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val lem1 = Thm.combination (Thm.reflexive (ct P)) surj_pair; 

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(*lemma "!!a b. PROP (a, b) ==> PROP P p"*) 

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val lem2 = prove_goalw_cterm [lem1] (ct (all_a_b ==> P $ p)) 

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(fn prems => [resolve_tac prems 1]); 
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5704  51 
(*lemma "!!a b. PROP (a, b) ==> !!x. PROP P x"*) 
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val lem3 = prove_goalw_cterm [] (ct (all_a_b ==> all_x)) 

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(fn prems => [rtac lem2 1, resolve_tac prems 1]); 
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5704  55 
(*lemma "!!x. PROP P x ==> !!a b. PROP (a, b)"*) 
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val lem4 = prove_goalw_cterm [] (ct (all_x ==> all_a_b)) 

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(fn prems => [resolve_tac prems 1]); 
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in standard (Thm.equal_intr lem4 lem3) end; 
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end; 