%   ORIGINAL: 'h4/thm/arithmetic/ABS_DIFF_SUMS_'
% 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: !n1 n2 m1 m2. 'h4/const/arithmetic/<=' ('h4/const/arithmetic/ABS_DIFF' ('h4/const/arithmetic/+' n1 n2) ('h4/const/arithmetic/+' m1 m2)) ('h4/const/arithmetic/+' ('h4/const/arithmetic/ABS_DIFF' n1 m1) ('h4/const/arithmetic/ABS_DIFF' n2 m2))
%   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: !n1 n2 m1 m2. 'h4/const/arithmetic/<=' ('h4/const/arithmetic/ABS_DIFF' ('h4/const/arithmetic/+' n1 n2) ('h4/const/arithmetic/+' m1 m2)) ('h4/const/arithmetic/+' ('h4/const/arithmetic/ABS_DIFF' n1 m1) ('h4/const/arithmetic/ABS_DIFF' n2 m2))
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_3f84967,V_3f84963]: ![F, G]: (![X]: s(V_3f84963,happ(s(fun(V_3f84967,V_3f84963),F),s(V_3f84967,X))) = s(V_3f84963,happ(s(fun(V_3f84967,V_3f84963),G),s(V_3f84967,X))) => s(fun(V_3f84967,V_3f84963),F) = s(fun(V_3f84967,V_3f84963),G))).
fof('h4/thm/arithmetic/ABS_DIFF_SUMS_', conjecture, ![N1, N2, M1, M2]: p(s(bool,'h4/const/arithmetic/<='(s('h4/type/num/num','h4/const/arithmetic/ABS_DIFF'(s('h4/type/num/num','h4/const/arithmetic/+'(s('h4/type/num/num',N1),s('h4/type/num/num',N2))),s('h4/type/num/num','h4/const/arithmetic/+'(s('h4/type/num/num',M1),s('h4/type/num/num',M2))))),s('h4/type/num/num','h4/const/arithmetic/+'(s('h4/type/num/num','h4/const/arithmetic/ABS_DIFF'(s('h4/type/num/num',N1),s('h4/type/num/num',M1))),s('h4/type/num/num','h4/const/arithmetic/ABS_DIFF'(s('h4/type/num/num',N2),s('h4/type/num/num',M2))))))))).
