%   ORIGINAL: 'h4/thm/pred_set/INJ_INL_'
% 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: !t s. (!x. 'h4/const/bool/IN' x s ==> 'h4/const/bool/IN' ('h4/const/sum/INL' x) t) ==> 'h4/const/pred_set/INJ' 'h4/const/sum/INL' s t
%   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: !t s. (!x. 'h4/const/bool/IN' x s ==> 'h4/const/bool/IN' (happ 'h4/const/sum/INL' x) t) ==> 'h4/const/pred_set/INJ' 'h4/const/sum/INL' s t
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_3f21421,V_3f21417]: ![F, G]: (![X]: s(V_3f21417,happ(s(fun(V_3f21421,V_3f21417),F),s(V_3f21421,X))) = s(V_3f21417,happ(s(fun(V_3f21421,V_3f21417),G),s(V_3f21421,X))) => s(fun(V_3f21421,V_3f21417),F) = s(fun(V_3f21421,V_3f21417),G))).
fof('h4/thm/pred_set/INJ_INL_', conjecture, ![A,B]: ![T, S]: (![X]: (p(s(bool,'h4/const/bool/IN'(s(A,X),s(fun(A,bool),S)))) => p(s(bool,'h4/const/bool/IN'(s('h4/type/sum/sum'(A,B),happ(s(fun(A,'h4/type/sum/sum'(A,B)),'h4/const/sum/INL'),s(A,X))),s(fun('h4/type/sum/sum'(A,B),bool),T))))) => p(s(bool,'h4/const/pred_set/INJ'(s(fun(A,'h4/type/sum/sum'(A,B)),'h4/const/sum/INL'),s(fun(A,bool),S),s(fun('h4/type/sum/sum'(A,B),bool),T)))))).
