%   ORIGINAL: 'h4/thm/relation/WeakLinearOrder_dichotomy_'
% 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: !R. 'h4/const/relation/WeakLinearOrder' R <=> 'h4/const/relation/WeakOrder' R /\ (!a b. R a b \/ R b a)
%   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: !R. 'h4/const/relation/WeakLinearOrder' R <=> 'h4/const/relation/WeakOrder' R /\ (!a b. happ (happ R a) b \/ happ (happ R b) a)
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_3f30128,V_3f30124]: ![F, G]: (![X]: s(V_3f30124,happ(s(fun(V_3f30128,V_3f30124),F),s(V_3f30128,X))) = s(V_3f30124,happ(s(fun(V_3f30128,V_3f30124),G),s(V_3f30128,X))) => s(fun(V_3f30128,V_3f30124),F) = s(fun(V_3f30128,V_3f30124),G))).
fof('h4/thm/relation/WeakLinearOrder_dichotomy_', conjecture, ![A]: ![R]: (p(s(bool,'h4/const/relation/WeakLinearOrder'(s(fun(A,fun(A,bool)),R)))) <=> (p(s(bool,'h4/const/relation/WeakOrder'(s(fun(A,fun(A,bool)),R)))) & ![A0, B]: (p(s(bool,happ(s(fun(A,bool),happ(s(fun(A,fun(A,bool)),R),s(A,A0))),s(A,B)))) | p(s(bool,happ(s(fun(A,bool),happ(s(fun(A,fun(A,bool)),R),s(A,B))),s(A,A0)))))))).
