%   ORIGINAL: 'h4/thm/sum/datatype_sum_'
% 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: !sum. 'h4/const/bool/DATATYPE' (sum 'h4/const/sum/INL' 'h4/const/sum/INR')
%   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: !sum. 'h4/const/bool/DATATYPE' (happ (happ sum 'h4/const/sum/INL') 'h4/const/sum/INR')
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_3f66636,V_3f66632]: ![F, G]: (![X]: s(V_3f66632,happ(s(fun(V_3f66636,V_3f66632),F),s(V_3f66636,X))) = s(V_3f66632,happ(s(fun(V_3f66636,V_3f66632),G),s(V_3f66636,X))) => s(fun(V_3f66636,V_3f66632),F) = s(fun(V_3f66636,V_3f66632),G))).
fof('h4/thm/sum/datatype_sum_', conjecture, ![C,A,B]: ![Sum]: p(s(bool,'h4/const/bool/DATATYPE'(s(C,happ(s(fun(fun(B,'h4/type/sum/sum'(A,B)),C),happ(s(fun(fun(A,'h4/type/sum/sum'(A,B)),fun(fun(B,'h4/type/sum/sum'(A,B)),C)),Sum),s(fun(A,'h4/type/sum/sum'(A,B)),'h4/const/sum/INL'))),s(fun(B,'h4/type/sum/sum'(A,B)),'h4/const/sum/INR'))))))).
