%   ORIGINAL: 'h4/thm/pred_set/BIJ_LINV_INV_'
% Assm: HL_TRUTH: T
% Assm: HL_FALSITY: ~F
% Assm: HL_BOOL_CASES: !t. (t <=> T) \/ (t <=> F)
% Assm: HL_EXT: !f g. (!x. f x = g x) ==> f = g
% Goal: !f s t. 'h4/const/pred_set/BIJ' f s t ==> (!x. 'h4/const/bool/IN' x t ==> f ('h4/const/pred_set/LINV' f s x) = x)
%   PROCESSED
% Assm ['HL_TRUTH']: T
% Assm ['HL_FALSITY']: ~F
% Assm ['HL_BOOL_CASES']: !t. (t <=> T) \/ (t <=> F)
% Assm ['HL_EXT']: !f g. (!x. happ f x = happ g x) ==> f = g
% Goal: !f s t. 'h4/const/pred_set/BIJ' f s t ==> (!x. 'h4/const/bool/IN' x t ==> happ f ('h4/const/pred_set/LINV' f s x) = x)
fof('HL_TRUTH', axiom, p(s(bool,'T'))).
fof('HL_FALSITY', axiom, ~ (p(s(bool,'F')))).
fof('HL_BOOL_CASES', axiom, ![T]: (s(bool,T) = s(bool,'T') | s(bool,T) = s(bool,'F'))).
fof('HL_EXT', axiom, ![V_3f18920,V_3f18916]: ![F, G]: (![X]: s(V_3f18916,happ(s(fun(V_3f18920,V_3f18916),F),s(V_3f18920,X))) = s(V_3f18916,happ(s(fun(V_3f18920,V_3f18916),G),s(V_3f18920,X))) => s(fun(V_3f18920,V_3f18916),F) = s(fun(V_3f18920,V_3f18916),G))).
fof('h4/thm/pred_set/BIJ_LINV_INV_', conjecture, ![A,B]: ![F, S, T]: (p(s(bool,'h4/const/pred_set/BIJ'(s(fun(A,B),F),s(fun(A,bool),S),s(fun(B,bool),T)))) => ![X]: (p(s(bool,'h4/const/bool/IN'(s(B,X),s(fun(B,bool),T)))) => s(B,happ(s(fun(A,B),F),s(A,'h4/const/pred_set/LINV'(s(fun(A,B),F),s(fun(A,bool),S),s(B,X))))) = s(B,X)))).
