WhoCites Definitions DiscreteMath Sections DiscrMathExt Doc
IF YOU CAN SEE THIS go to /sfa/Nuprl/Shared/Xindentation_hack_doc.html
One-to-one correspondence between index families of classes.

Who Cites one one corr fams?
one_one_corr_famsDef  (x:AB(x)) ~ (x':A'B'(x'))
Def  == f:(AA'), g:(A'A), F:(x:AB(x)B'(f(x))), G:(x:AB'(f(x))B(x)).
Def  == InvFuns(A;A';f;g) & (u:A. InvFuns(B(u);B'(f(u));F(u);G(u)))
Thm*  A:Type, A':Type, B:(AType), B':(A'Type).
Thm*  ((x:AB(x)) ~ (x':A'B'(x')))  Prop
inv_funs_2Def  InvFuns(A;B;f;g) == (x:Ag(f(x)) = x) & (y:Bf(g(y)) = y)
Thm*  f:(AB), g:(BA). InvFuns(A;B;f;g Prop

Syntax:(x:AB(x)) ~ (x':A'B'(x')) has structure: one_one_corr_fams(AA'x.B(x); x'.B'(x'))

About:
applyfunctionuniverseequalmemberprop
andallexists!abstraction
IF YOU CAN SEE THIS go to /sfa/Nuprl/Shared/Xindentation_hack_doc.html

WhoCites Definitions DiscreteMath Sections DiscrMathExt Doc