%   ORIGINAL: 'h4/thm/pred_set/INJ_ID_'
% 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: !s. 'h4/const/pred_set/INJ' (\x. x) s s
%   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: !_0. (!x. happ _0 x = x) ==> (!s. 'h4/const/pred_set/INJ' _0 s s)
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_3f18445,V_3f18441]: ![F, G]: (![X]: s(V_3f18441,happ(s(fun(V_3f18445,V_3f18441),F),s(V_3f18445,X))) = s(V_3f18441,happ(s(fun(V_3f18445,V_3f18441),G),s(V_3f18445,X))) => s(fun(V_3f18445,V_3f18441),F) = s(fun(V_3f18445,V_3f18441),G))).
fof('h4/thm/pred_set/INJ_ID_', conjecture, ![A]: ![V__0]: (![X]: s(A,happ(s(fun(A,A),V__0),s(A,X))) = s(A,X) => ![S]: p(s(bool,'h4/const/pred_set/INJ'(s(fun(A,A),V__0),s(fun(A,bool),S),s(fun(A,bool),S)))))).
