Thm* e:(B B).
Thm* ( b:B. e(b) = b)
Thm* 
Thm* ( A:Type, f:(A A B). ( a:A. (Diag f wrt x. e(x)) = f(a))) | [diagonalization_wrt_eq] |
Thm* R:(B B Prop), e:(B B).
Thm* ( b:B. R(e(b),b))
Thm* 
Thm* ( A:Type, f:(A A B). ( a:A. R((Diag f wrt x. e(x))(a),f(a,a)))) | [diagonalization] |
Thm* f:(A B). f A {y:B| x:A. f(x) = y } | [range_restriction_indep] |
Thm* ( x:A. !y:B. P(x,y))  ( f:(A B). x:A. P(x,f(x))) | [indep_fun_description] |
Thm* ( x:A. y:B. Q(x,y))  ( f:(A B). x:A. Q(x,f(x))) | [ax_choice_version3] |
Thm* ( x:A. y:B. Q(x,y))  ( f:(A B). x:A. Q(x,f(x))) | [ax_choice_version2] |
Thm* ( x:A. !y:B(x). P(x,y))  ( f:(x:A B(x)). x:A. P(x,f(x))) | [fun_description] |
Thm* ( x:A. y:B(x). Q(x,y))  ( f:(x:A B(x)). x:A. Q(x,f(x))) | [dep_ax_choice_version2] |
Thm* ( x:T. Dec(E(x)))  ( f:(T  ). x:T. f(x)  E(x)) | [dec_pred_iff_some_boolfun] |
Thm* ( Set:Type, :(Set Set Prop).
Thm* ( P:(Set Prop). p:Set. x:Set. (x p)  P(x)) | [RussellsParadox_Frege2] |
Thm* ( A:Type, Q:(A A Prop). P:(A Prop). p:A. x:A. Q(x,p)  P(x)) | [RussellsParadox_Frege] |
Thm* (A Discrete)  ( e:(A A  ). IsEqFun(A;e)) | [discrete_vs_bool2] |
Thm* (A Discrete)  ( e:(A A  ). x,y:A. (x e y)  x = y) | [discrete_vs_bool] |
Thm* ( ! A)  ( x:A. y:A. x = y) | [inhabited_uniquely_elim] |
Thm* ( ! A)  ( x:A. y:A. x = y) | [inhabited_uniquely_vs_exists] |
Thm* ( A)  ( x:A. True) | [inhabited_vs_exists] |
Thm* A:Type. P = ( A) Prop | [inhab_rep_axiom] |
Thm* ( x:T. Q(x))  ( x:T. Q(x)) | [not_over_exists_imp] |
Thm* Dec(P)  ( b: . b  P) | [decbl_iff_some_bool] |
Def !x:A. P(x) == x:A. x is the x:A. P(x) | [exists_unique] |