%   ORIGINAL: 'h4/thm/transc/TAN_SEC_'
% 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. ~('h4/const/transc/cos' x = 'h4/const/real/real_of_num' 'h4/const/num/0') ==> 'h4/const/realax/real_add' ('h4/const/real/real_of_num' ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' 'h4/const/arithmetic/ZERO'))) ('h4/const/real/pow' ('h4/const/transc/tan' x) ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT2' 'h4/const/arithmetic/ZERO'))) = 'h4/const/real/pow' ('h4/const/realax/inv' ('h4/const/transc/cos' x)) ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT2' 'h4/const/arithmetic/ZERO'))
%   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. ~('h4/const/transc/cos' x = 'h4/const/real/real_of_num' 'h4/const/num/0') ==> 'h4/const/realax/real_add' ('h4/const/real/real_of_num' ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' 'h4/const/arithmetic/ZERO'))) ('h4/const/real/pow' ('h4/const/transc/tan' x) ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT2' 'h4/const/arithmetic/ZERO'))) = 'h4/const/real/pow' ('h4/const/realax/inv' ('h4/const/transc/cos' x)) ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT2' 'h4/const/arithmetic/ZERO'))
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_3f72086,V_3f72082]: ![F, G]: (![X]: s(V_3f72082,happ(s(fun(V_3f72086,V_3f72082),F),s(V_3f72086,X))) = s(V_3f72082,happ(s(fun(V_3f72086,V_3f72082),G),s(V_3f72086,X))) => s(fun(V_3f72086,V_3f72082),F) = s(fun(V_3f72086,V_3f72082),G))).
fof('h4/thm/transc/TAN_SEC_', conjecture, ![X]: (~ (s('h4/type/realax/real','h4/const/transc/cos'(s('h4/type/realax/real',X))) = s('h4/type/realax/real','h4/const/real/real_of_num'(s('h4/type/num/num','h4/const/num/0')))) => s('h4/type/realax/real','h4/const/realax/real_add'(s('h4/type/realax/real','h4/const/real/real_of_num'(s('h4/type/num/num','h4/const/arithmetic/NUMERAL'(s('h4/type/num/num','h4/const/arithmetic/BIT1'(s('h4/type/num/num','h4/const/arithmetic/ZERO'))))))),s('h4/type/realax/real','h4/const/real/pow'(s('h4/type/realax/real','h4/const/transc/tan'(s('h4/type/realax/real',X))),s('h4/type/num/num','h4/const/arithmetic/NUMERAL'(s('h4/type/num/num','h4/const/arithmetic/BIT2'(s('h4/type/num/num','h4/const/arithmetic/ZERO'))))))))) = s('h4/type/realax/real','h4/const/real/pow'(s('h4/type/realax/real','h4/const/realax/inv'(s('h4/type/realax/real','h4/const/transc/cos'(s('h4/type/realax/real',X))))),s('h4/type/num/num','h4/const/arithmetic/NUMERAL'(s('h4/type/num/num','h4/const/arithmetic/BIT2'(s('h4/type/num/num','h4/const/arithmetic/ZERO'))))))))).
