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(* Title: Cube/cube


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ID: $Id$


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Author: Tobias Nipkow


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Copyright 1990 University of Cambridge


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For cube.thy. The systems of the Lambdacube that extend simple types


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*)


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open Cube;


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val simple = [s_b,strip_s,strip_b,app,lam_ss,pi_ss];


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val L2_thy = extend_theory Cube.thy "L2" ([],[],[],[],[],[],None)

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[


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("pi_bs", "[ A:[]; !!x. x:A ==> B(x):* ] ==> Prod(A,B):*"),


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("lam_bs", "[ A:[]; !!x. x:A ==> f(x):B(x); !!x. x:A ==> B(x):* ] \


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\ ==> Abs(A,f) : Prod(A,B)")


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];


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val lam_bs = get_axiom L2_thy "lam_bs";


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val pi_bs = get_axiom L2_thy "pi_bs";


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val L2 = simple @ [lam_bs,pi_bs];


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val Lomega_thy = extend_theory Cube.thy "Lomega" ([],[],[],[],[],[],None)

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[


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("pi_bb", "[ A:[]; !!x. x:A ==> B(x):[] ] ==> Prod(A,B):[]"),


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("lam_bb", "[ A:[]; !!x. x:A ==> f(x):B(x); !!x. x:A ==> B(x):[] ] \


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\ ==> Abs(A,f) : Prod(A,B)")


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];


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val lam_bb = get_axiom Lomega_thy "lam_bb";


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val pi_bb = get_axiom Lomega_thy "pi_bb";


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val Lomega = simple @ [lam_bb,pi_bb];


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val LOmega_thy = merge_theories(L2_thy,Lomega_thy);


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val LOmega = simple @ [lam_bs,pi_bs,lam_bb,pi_bb];


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val LP_thy = extend_theory Cube.thy "LP" ([],[],[],[],[],[],None)

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[


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("pi_sb", "[ A:*; !!x. x:A ==> B(x):[] ] ==> Prod(A,B):[]"),


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("lam_sb", "[ A:*; !!x. x:A ==> f(x):B(x); !!x. x:A ==> B(x):[] ] \


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\ ==> Abs(A,f) : Prod(A,B)")


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];


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val lam_sb = get_axiom LP_thy "lam_sb";


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val pi_sb = get_axiom LP_thy "pi_sb";


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val LP = simple @ [lam_sb,pi_sb];


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val LP2_thy = merge_theories(L2_thy,LP_thy);


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val LP2 = simple @ [lam_bs,pi_bs,lam_sb,pi_sb];


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val LPomega_thy = merge_theories(LP_thy,Lomega_thy);


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val LPomega = simple @ [lam_bb,pi_bb,lam_sb,pi_sb];


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val CC_thy = merge_theories(L2_thy,LPomega_thy);


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val CC = simple @ [lam_bs,pi_bs,lam_bb,pi_bb,lam_sb,pi_sb];
