%   ORIGINAL: 'h4/thm/quotient_sum/SUM_REL_def_1'
% 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: !b2 b1 R2 R1. 'h4/const/quotient_sum/+++' R1 R2 ('h4/const/sum/INR' b1) ('h4/const/sum/INR' b2) <=> R2 b1 b2
%   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: !b2 b1 R2 R1. 'h4/const/quotient_sum/+++' R1 R2 ('h4/const/sum/INR' b1) ('h4/const/sum/INR' b2) <=> happ (happ R2 b1) b2
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_3f14219,V_3f14215]: ![F, G]: (![X]: s(V_3f14215,happ(s(fun(V_3f14219,V_3f14215),F),s(V_3f14219,X))) = s(V_3f14215,happ(s(fun(V_3f14219,V_3f14215),G),s(V_3f14219,X))) => s(fun(V_3f14219,V_3f14215),F) = s(fun(V_3f14219,V_3f14215),G))).
fof('h4/thm/quotient_sum/SUM_REL_def_1', conjecture, ![A,B]: ![B2, B1, R2, R1]: s(bool,'h4/const/quotient_sum/+++'(s(fun(A,fun(A,bool)),R1),s(fun(B,fun(B,bool)),R2),s('h4/type/sum/sum'(A,B),'h4/const/sum/INR'(s(B,B1))),s('h4/type/sum/sum'(A,B),'h4/const/sum/INR'(s(B,B2))))) = s(bool,happ(s(fun(B,bool),happ(s(fun(B,fun(B,bool)),R2),s(B,B1))),s(B,B2)))).
