%   ORIGINAL: 'h4/thm/arithmetic/EXP_BASE_LEQ_MONO_SUC_IMP_'
% 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: !n m b. 'h4/const/arithmetic/<=' m n ==> 'h4/const/arithmetic/<=' ('h4/const/arithmetic/EXP' ('h4/const/num/SUC' b) m) ('h4/const/arithmetic/EXP' ('h4/const/num/SUC' b) 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: !n m b. 'h4/const/arithmetic/<=' m n ==> 'h4/const/arithmetic/<=' ('h4/const/arithmetic/EXP' ('h4/const/num/SUC' b) m) ('h4/const/arithmetic/EXP' ('h4/const/num/SUC' b) 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_3f83566,V_3f83562]: ![F, G]: (![X]: s(V_3f83562,happ(s(fun(V_3f83566,V_3f83562),F),s(V_3f83566,X))) = s(V_3f83562,happ(s(fun(V_3f83566,V_3f83562),G),s(V_3f83566,X))) => s(fun(V_3f83566,V_3f83562),F) = s(fun(V_3f83566,V_3f83562),G))).
fof('h4/thm/arithmetic/EXP_BASE_LEQ_MONO_SUC_IMP_', conjecture, ![N, M, B]: (p(s(bool,'h4/const/arithmetic/<='(s('h4/type/num/num',M),s('h4/type/num/num',N)))) => p(s(bool,'h4/const/arithmetic/<='(s('h4/type/num/num','h4/const/arithmetic/EXP'(s('h4/type/num/num','h4/const/num/SUC'(s('h4/type/num/num',B))),s('h4/type/num/num',M))),s('h4/type/num/num','h4/const/arithmetic/EXP'(s('h4/type/num/num','h4/const/num/SUC'(s('h4/type/num/num',B))),s('h4/type/num/num',N)))))))).
