author  paulson 
Wed, 15 Jul 1998 14:13:18 +0200  
changeset 5147  825877190618 
parent 5068  fb28eaa07e01 
child 5241  e5129172cb2b 
permissions  rwrr 
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(* Title: ZF/AC/AC1_WO2.ML 
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ID: $Id$ 
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Author: Krzysztof Grabczewski 
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The proof of AC1 ==> WO2 

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*) 

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open AC1_WO2; 

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(*Establishing the existence of a bijection  hence the need for uresult*) 
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val [prem] = goal thy "f : (PROD X:Pow(x)  {0}. X) ==> \ 
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\ ?g(f) : bij(x, LEAST i. HH(lam X:Pow(x){0}. {f`X}, x, i) = {x})"; 
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by (resolve_tac [bij_Least_HH_x RS bij_converse_bij] 1); 
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by (rtac f_subsets_imp_UN_HH_eq_x 1); 
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by (resolve_tac [lam_type RS apply_type] 1 THEN (assume_tac 2)); 
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by (fast_tac (claset() addSDs [equals0D, prem RS apply_type]) 1); 
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by (fast_tac (claset() addSIs [prem RS Pi_weaken_type]) 1); 

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val lemma1 = uresult() > standard; 
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5147
825877190618
More tidying and removal of "\!\!... from Goal commands
paulson
parents:
5068
diff
changeset

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Goalw [AC1_def, WO2_def, eqpoll_def] "AC1 ==> WO2"; 
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by (rtac allI 1); 
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by (eres_inst_tac [("x","Pow(A){0}")] allE 1); 
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by (fast_tac (claset() addSDs [lemma1] addSIs [Ord_Least]) 1); 
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qed "AC1_WO2"; 