%   ORIGINAL: 'h4/thm/real/REAL_SUB_'
% 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: !m n. 'h4/const/real/real_sub' ('h4/const/real/real_of_num' m) ('h4/const/real/real_of_num' n) = 'h4/const/bool/COND' ('h4/const/arithmetic/-' m n = 'h4/const/num/0') ('h4/const/realax/real_neg' ('h4/const/real/real_of_num' ('h4/const/arithmetic/-' n m))) ('h4/const/real/real_of_num' ('h4/const/arithmetic/-' m n))
%   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: !m n. ?v. (v <=> 'h4/const/arithmetic/-' m n = 'h4/const/num/0') /\ 'h4/const/real/real_sub' ('h4/const/real/real_of_num' m) ('h4/const/real/real_of_num' n) = 'h4/const/bool/COND' v ('h4/const/realax/real_neg' ('h4/const/real/real_of_num' ('h4/const/arithmetic/-' n m))) ('h4/const/real/real_of_num' ('h4/const/arithmetic/-' m n))
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_3f95694,V_3f95690]: ![F, G]: (![X]: s(V_3f95690,happ(s(fun(V_3f95694,V_3f95690),F),s(V_3f95694,X))) = s(V_3f95690,happ(s(fun(V_3f95694,V_3f95690),G),s(V_3f95694,X))) => s(fun(V_3f95694,V_3f95690),F) = s(fun(V_3f95694,V_3f95690),G))).
fof('h4/thm/real/REAL_SUB_', conjecture, ![M, N]: ?[V]: ((p(s(bool,V)) <=> s('h4/type/num/num','h4/const/arithmetic/-'(s('h4/type/num/num',M),s('h4/type/num/num',N))) = s('h4/type/num/num','h4/const/num/0')) & s('h4/type/realax/real','h4/const/real/real_sub'(s('h4/type/realax/real','h4/const/real/real_of_num'(s('h4/type/num/num',M))),s('h4/type/realax/real','h4/const/real/real_of_num'(s('h4/type/num/num',N))))) = s('h4/type/realax/real','h4/const/bool/COND'(s(bool,V),s('h4/type/realax/real','h4/const/realax/real_neg'(s('h4/type/realax/real','h4/const/real/real_of_num'(s('h4/type/num/num','h4/const/arithmetic/-'(s('h4/type/num/num',N),s('h4/type/num/num',M))))))),s('h4/type/realax/real','h4/const/real/real_of_num'(s('h4/type/num/num','h4/const/arithmetic/-'(s('h4/type/num/num',M),s('h4/type/num/num',N))))))))).
