%   ORIGINAL: 'h4/thm/quotient/RESPECTS_o_'
% 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: !R1 R2 R3 f g. 'h4/const/quotient/respects' ('h4/const/quotient/===>' R2 R3) f /\ 'h4/const/quotient/respects' ('h4/const/quotient/===>' R1 R2) g ==> 'h4/const/quotient/respects' ('h4/const/quotient/===>' R1 R3) ('h4/const/combin/o' f 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: !R1 R2 R3 f g. 'h4/const/quotient/respects' ('h4/const/quotient/===>' R2 R3) f /\ 'h4/const/quotient/respects' ('h4/const/quotient/===>' R1 R2) g ==> 'h4/const/quotient/respects' ('h4/const/quotient/===>' R1 R3) ('h4/const/combin/o' 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_3f74965,V_3f74961]: ![F, G]: (![X]: s(V_3f74961,happ(s(fun(V_3f74965,V_3f74961),F),s(V_3f74965,X))) = s(V_3f74961,happ(s(fun(V_3f74965,V_3f74961),G),s(V_3f74965,X))) => s(fun(V_3f74965,V_3f74961),F) = s(fun(V_3f74965,V_3f74961),G))).
fof('h4/thm/quotient/RESPECTS_o_', conjecture, ![C,A,B]: ![R1, R2, R3, F, G]: ((p(s(bool,'h4/const/quotient/respects'(s(fun(fun(B,C),fun(fun(B,C),bool)),'h4/const/quotient/===>'(s(fun(B,fun(B,bool)),R2),s(fun(C,fun(C,bool)),R3))),s(fun(B,C),F)))) & p(s(bool,'h4/const/quotient/respects'(s(fun(fun(A,B),fun(fun(A,B),bool)),'h4/const/quotient/===>'(s(fun(A,fun(A,bool)),R1),s(fun(B,fun(B,bool)),R2))),s(fun(A,B),G))))) => p(s(bool,'h4/const/quotient/respects'(s(fun(fun(A,C),fun(fun(A,C),bool)),'h4/const/quotient/===>'(s(fun(A,fun(A,bool)),R1),s(fun(C,fun(C,bool)),R3))),s(fun(A,C),'h4/const/combin/o'(s(fun(B,C),F),s(fun(A,B),G)))))))).
