%   ORIGINAL: 'h4/thm/arithmetic/LESS_EQ_LESS_EQ_MONO_'
% 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 p q. 'h4/const/arithmetic/<=' m p /\ 'h4/const/arithmetic/<=' n q ==> 'h4/const/arithmetic/<=' ('h4/const/arithmetic/+' m n) ('h4/const/arithmetic/+' p q)
%   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 p q. 'h4/const/arithmetic/<=' m p /\ 'h4/const/arithmetic/<=' n q ==> 'h4/const/arithmetic/<=' ('h4/const/arithmetic/+' m n) ('h4/const/arithmetic/+' p q)
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_3f78641,V_3f78637]: ![F, G]: (![X]: s(V_3f78637,happ(s(fun(V_3f78641,V_3f78637),F),s(V_3f78641,X))) = s(V_3f78637,happ(s(fun(V_3f78641,V_3f78637),G),s(V_3f78641,X))) => s(fun(V_3f78641,V_3f78637),F) = s(fun(V_3f78641,V_3f78637),G))).
fof('h4/thm/arithmetic/LESS_EQ_LESS_EQ_MONO_', conjecture, ![M, N, P, Q]: ((p(s(bool,'h4/const/arithmetic/<='(s('h4/type/num/num',M),s('h4/type/num/num',P)))) & p(s(bool,'h4/const/arithmetic/<='(s('h4/type/num/num',N),s('h4/type/num/num',Q))))) => p(s(bool,'h4/const/arithmetic/<='(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/arithmetic/+'(s('h4/type/num/num',P),s('h4/type/num/num',Q)))))))).
