%   ORIGINAL: 'h4/thm/hrat/TRAT_ADD_WELLDEFINED2_'
% 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: !p1 p2 q1 q2. 'h4/const/hrat/trat_eq' p1 p2 /\ 'h4/const/hrat/trat_eq' q1 q2 ==> 'h4/const/hrat/trat_eq' ('h4/const/hrat/trat_add' p1 q1) ('h4/const/hrat/trat_add' p2 q2)
%   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: !p1 p2 q1 q2. 'h4/const/hrat/trat_eq' p1 p2 /\ 'h4/const/hrat/trat_eq' q1 q2 ==> 'h4/const/hrat/trat_eq' ('h4/const/hrat/trat_add' p1 q1) ('h4/const/hrat/trat_add' p2 q2)
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_3f13369,V_3f13365]: ![F, G]: (![X]: s(V_3f13365,happ(s(fun(V_3f13369,V_3f13365),F),s(V_3f13369,X))) = s(V_3f13365,happ(s(fun(V_3f13369,V_3f13365),G),s(V_3f13369,X))) => s(fun(V_3f13369,V_3f13365),F) = s(fun(V_3f13369,V_3f13365),G))).
fof('h4/thm/hrat/TRAT_ADD_WELLDEFINED2_', conjecture, ![P1, P2, Q1, Q2]: ((p(s(bool,'h4/const/hrat/trat_eq'(s('h4/type/pair/prod'('h4/type/num/num','h4/type/num/num'),P1),s('h4/type/pair/prod'('h4/type/num/num','h4/type/num/num'),P2)))) & p(s(bool,'h4/const/hrat/trat_eq'(s('h4/type/pair/prod'('h4/type/num/num','h4/type/num/num'),Q1),s('h4/type/pair/prod'('h4/type/num/num','h4/type/num/num'),Q2))))) => p(s(bool,'h4/const/hrat/trat_eq'(s('h4/type/pair/prod'('h4/type/num/num','h4/type/num/num'),'h4/const/hrat/trat_add'(s('h4/type/pair/prod'('h4/type/num/num','h4/type/num/num'),P1),s('h4/type/pair/prod'('h4/type/num/num','h4/type/num/num'),Q1))),s('h4/type/pair/prod'('h4/type/num/num','h4/type/num/num'),'h4/const/hrat/trat_add'(s('h4/type/pair/prod'('h4/type/num/num','h4/type/num/num'),P2),s('h4/type/pair/prod'('h4/type/num/num','h4/type/num/num'),Q2)))))))).
