Some definitions of interest.
biject	Def  Bij(A; B; f) == Inj(A; B; f) & Surj(A; B; f)
	Thm*  A,B:Type, f:(AB). Bij(A; B; f)  Prop
one_one_corr_fams	Def  (x:A. B(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:A. B(x)) ~ (x':A'. B'(x')))  Prop

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