%   ORIGINAL: 'h4/thm/hrat/HRAT_ADD_TOTAL_'
% 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: !h i. h = i \/ (?d. h = 'h4/const/hrat/hrat_add' i d) \/ (?d. i = 'h4/const/hrat/hrat_add' h d)
%   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: !h i. h = i \/ (?d. h = 'h4/const/hrat/hrat_add' i d) \/ (?d. i = 'h4/const/hrat/hrat_add' h d)
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_3f14069,V_3f14065]: ![F, G]: (![X]: s(V_3f14065,happ(s(fun(V_3f14069,V_3f14065),F),s(V_3f14069,X))) = s(V_3f14065,happ(s(fun(V_3f14069,V_3f14065),G),s(V_3f14069,X))) => s(fun(V_3f14069,V_3f14065),F) = s(fun(V_3f14069,V_3f14065),G))).
fof('h4/thm/hrat/HRAT_ADD_TOTAL_', conjecture, ![H, I]: (s('h4/type/hrat/hrat',H) = s('h4/type/hrat/hrat',I) | (?[D]: s('h4/type/hrat/hrat',H) = s('h4/type/hrat/hrat','h4/const/hrat/hrat_add'(s('h4/type/hrat/hrat',I),s('h4/type/hrat/hrat',D))) | ?[D]: s('h4/type/hrat/hrat',I) = s('h4/type/hrat/hrat','h4/const/hrat/hrat_add'(s('h4/type/hrat/hrat',H),s('h4/type/hrat/hrat',D)))))).
