%   ORIGINAL: 'h4/thm/sum/sum_axiom_'
% 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: !f g. 'h4/const/bool/?!' (\h. 'h4/const/combin/o' h 'h4/const/sum/INL' = f /\ 'h4/const/combin/o' h 'h4/const/sum/INR' = g)
%   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. (!f g h. happ (happ (happ _0 f) g) h <=> 'h4/const/combin/o' h 'h4/const/sum/INL' = f /\ 'h4/const/combin/o' h 'h4/const/sum/INR' = g) ==> (!f g. 'h4/const/bool/?!' (happ (happ _0 f) g))
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_3f66111,V_3f66107]: ![F, G]: (![X]: s(V_3f66107,happ(s(fun(V_3f66111,V_3f66107),F),s(V_3f66111,X))) = s(V_3f66107,happ(s(fun(V_3f66111,V_3f66107),G),s(V_3f66111,X))) => s(fun(V_3f66111,V_3f66107),F) = s(fun(V_3f66111,V_3f66107),G))).
fof('h4/thm/sum/sum_axiom_', conjecture, ![A,B,C]: ![V__0]: (![F, G, H]: (p(s(bool,happ(s(fun(fun('h4/type/sum/sum'(A,B),C),bool),happ(s(fun(fun(B,C),fun(fun('h4/type/sum/sum'(A,B),C),bool)),happ(s(fun(fun(A,C),fun(fun(B,C),fun(fun('h4/type/sum/sum'(A,B),C),bool))),V__0),s(fun(A,C),F))),s(fun(B,C),G))),s(fun('h4/type/sum/sum'(A,B),C),H)))) <=> (s(fun(A,C),'h4/const/combin/o'(s(fun('h4/type/sum/sum'(A,B),C),H),s(fun(A,'h4/type/sum/sum'(A,B)),'h4/const/sum/INL'))) = s(fun(A,C),F) & s(fun(B,C),'h4/const/combin/o'(s(fun('h4/type/sum/sum'(A,B),C),H),s(fun(B,'h4/type/sum/sum'(A,B)),'h4/const/sum/INR'))) = s(fun(B,C),G))) => ![F, G]: p(s(bool,'h4/const/bool/?!'(s(fun(fun('h4/type/sum/sum'(A,B),C),bool),happ(s(fun(fun(B,C),fun(fun('h4/type/sum/sum'(A,B),C),bool)),happ(s(fun(fun(A,C),fun(fun(B,C),fun(fun('h4/type/sum/sum'(A,B),C),bool))),V__0),s(fun(A,C),F))),s(fun(B,C),G)))))))).
