src/ZF/qpair.thy
changeset 120 09287f26bfb8
parent 44 00597b21a6a9
child 124 858ab9a9b047
equal deleted inserted replaced
119:0e58da397b1d 120:09287f26bfb8
    29   "QSUM x:A. B"  => "QSigma(A, %x. B)"
    29   "QSUM x:A. B"  => "QSigma(A, %x. B)"
    30   "A <*> B"      => "QSigma(A, _K(B))"
    30   "A <*> B"      => "QSigma(A, _K(B))"
    31 
    31 
    32 rules
    32 rules
    33   QPair_def       "<a;b> == a+b"
    33   QPair_def       "<a;b> == a+b"
    34   qsplit_def      "qsplit(c,p)  ==  THE y. EX a b. p=<a;b> & y=c(a,b)"
    34   qsplit_def      "qsplit(c,p)  == THE y. EX a b. p=<a;b> & y=c(a,b)"
    35   qfsplit_def     "qfsplit(R,z) == EX x y. z=<x;y> & R(x,y)"
    35   qfsplit_def     "qfsplit(R,z) == EX x y. z=<x;y> & R(x,y)"
    36   qconverse_def   "qconverse(r) == {z. w:r, EX x y. w=<x;y> & z=<y;x>}"
    36   qconverse_def   "qconverse(r) == {z. w:r, EX x y. w=<x;y> & z=<y;x>}"
    37   QSigma_def      "QSigma(A,B)  ==  UN x:A. UN y:B(x). {<x;y>}"
    37   QSigma_def      "QSigma(A,B)  ==  UN x:A. UN y:B(x). {<x;y>}"
    38 
    38 
    39   qsum_def        "A <+> B      == QSigma({0}, %x.A) Un QSigma({1}, %x.B)"
    39   qsum_def        "A <+> B      == ({0} <*> A) Un ({1} <*> B)"
    40   QInl_def        "QInl(a)      == <0;a>"
    40   QInl_def        "QInl(a)      == <0;a>"
    41   QInr_def        "QInr(b)      == <1;b>"
    41   QInr_def        "QInr(b)      == <1;b>"
    42   qcase_def       "qcase(c,d)   == qsplit(%y z. cond(y, d(z), c(z)))"
    42   qcase_def       "qcase(c,d)   == qsplit(%y z. cond(y, d(z), c(z)))"
    43 end
    43 end
    44 
    44