%   ORIGINAL: 'h4/thm/pair/datatype_pair_'
% 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: !pair. 'h4/const/bool/DATATYPE' (pair 'h4/const/pair/,')
%   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: !pair. 'h4/const/bool/DATATYPE' (happ pair 'h4/const/pair/,')
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_3f61711,V_3f61707]: ![F, G]: (![X]: s(V_3f61707,happ(s(fun(V_3f61711,V_3f61707),F),s(V_3f61711,X))) = s(V_3f61707,happ(s(fun(V_3f61711,V_3f61707),G),s(V_3f61711,X))) => s(fun(V_3f61711,V_3f61707),F) = s(fun(V_3f61711,V_3f61707),G))).
fof('h4/thm/pair/datatype_pair_', conjecture, ![C,A,B]: ![Pair]: p(s(bool,'h4/const/bool/DATATYPE'(s(C,happ(s(fun(fun(A,fun(B,'h4/type/pair/prod'(A,B))),C),Pair),s(fun(A,fun(B,'h4/type/pair/prod'(A,B))),'h4/const/pair/,'))))))).
