%   ORIGINAL: 'h4/thm/arithmetic/NRC_ADD_EQN_'
% 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: !z x n m R. 'h4/const/arithmetic/NRC' R ('h4/const/arithmetic/+' m n) x z <=> (?y. 'h4/const/arithmetic/NRC' R m x y /\ 'h4/const/arithmetic/NRC' R n y z)
%   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: !z x n m R. 'h4/const/arithmetic/NRC' R ('h4/const/arithmetic/+' m n) x z <=> (?y. 'h4/const/arithmetic/NRC' R m x y /\ 'h4/const/arithmetic/NRC' R n y z)
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_3f85192,V_3f85188]: ![F, G]: (![X]: s(V_3f85188,happ(s(fun(V_3f85192,V_3f85188),F),s(V_3f85192,X))) = s(V_3f85188,happ(s(fun(V_3f85192,V_3f85188),G),s(V_3f85192,X))) => s(fun(V_3f85192,V_3f85188),F) = s(fun(V_3f85192,V_3f85188),G))).
fof('h4/thm/arithmetic/NRC_ADD_EQN_', conjecture, ![A]: ![Z, X, N, M, R]: (p(s(bool,'h4/const/arithmetic/NRC'(s(fun(A,fun(A,bool)),R),s('h4/type/num/num','h4/const/arithmetic/+'(s('h4/type/num/num',M),s('h4/type/num/num',N))),s(A,X),s(A,Z)))) <=> ?[Y]: (p(s(bool,'h4/const/arithmetic/NRC'(s(fun(A,fun(A,bool)),R),s('h4/type/num/num',M),s(A,X),s(A,Y)))) & p(s(bool,'h4/const/arithmetic/NRC'(s(fun(A,fun(A,bool)),R),s('h4/type/num/num',N),s(A,Y),s(A,Z))))))).
