%   ORIGINAL: 'h4/thm/relation/inv_image_thm_'
% 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: !R f x y. 'h4/const/relation/inv_image' R f x y <=> R (f x) (f y)
%   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: !R f x y. 'h4/const/relation/inv_image' R f x y <=> happ (happ R (happ f x)) (happ f y)
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_3f28178,V_3f28174]: ![F, G]: (![X]: s(V_3f28174,happ(s(fun(V_3f28178,V_3f28174),F),s(V_3f28178,X))) = s(V_3f28174,happ(s(fun(V_3f28178,V_3f28174),G),s(V_3f28178,X))) => s(fun(V_3f28178,V_3f28174),F) = s(fun(V_3f28178,V_3f28174),G))).
fof('h4/thm/relation/inv_image_thm_', conjecture, ![B,A]: ![R, F, X, Y]: s(bool,'h4/const/relation/inv_image'(s(fun(B,fun(B,bool)),R),s(fun(A,B),F),s(A,X),s(A,Y))) = s(bool,happ(s(fun(B,bool),happ(s(fun(B,fun(B,bool)),R),s(B,happ(s(fun(A,B),F),s(A,X))))),s(B,happ(s(fun(A,B),F),s(A,Y)))))).
