%   ORIGINAL: 'h4/thm/poly/POLY_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: !x k p. 'h4/const/real/real_lte' ('h4/const/real/abs' x) k ==> 'h4/const/real/real_lte' ('h4/const/real/abs' ('h4/const/poly/poly' p x)) ('h4/const/poly/poly' ('h4/const/list/MAP' 'h4/const/real/abs' p) k)
%   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: !x k p. 'h4/const/real/real_lte' (happ 'h4/const/real/abs' x) k ==> 'h4/const/real/real_lte' (happ 'h4/const/real/abs' ('h4/const/poly/poly' p x)) ('h4/const/poly/poly' ('h4/const/list/MAP' 'h4/const/real/abs' p) k)
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_3f48136,V_3f48132]: ![F, G]: (![X]: s(V_3f48132,happ(s(fun(V_3f48136,V_3f48132),F),s(V_3f48136,X))) = s(V_3f48132,happ(s(fun(V_3f48136,V_3f48132),G),s(V_3f48136,X))) => s(fun(V_3f48136,V_3f48132),F) = s(fun(V_3f48136,V_3f48132),G))).
fof('h4/thm/poly/POLY_MONO_', conjecture, ![X, K, P]: (p(s(bool,'h4/const/real/real_lte'(s('h4/type/realax/real',happ(s(fun('h4/type/realax/real','h4/type/realax/real'),'h4/const/real/abs'),s('h4/type/realax/real',X))),s('h4/type/realax/real',K)))) => p(s(bool,'h4/const/real/real_lte'(s('h4/type/realax/real',happ(s(fun('h4/type/realax/real','h4/type/realax/real'),'h4/const/real/abs'),s('h4/type/realax/real','h4/const/poly/poly'(s('h4/type/list/list'('h4/type/realax/real'),P),s('h4/type/realax/real',X))))),s('h4/type/realax/real','h4/const/poly/poly'(s('h4/type/list/list'('h4/type/realax/real'),'h4/const/list/MAP'(s(fun('h4/type/realax/real','h4/type/realax/real'),'h4/const/real/abs'),s('h4/type/list/list'('h4/type/realax/real'),P))),s('h4/type/realax/real',K)))))))).
