%   ORIGINAL: 'h4/thm/option/OPTION_BIND_EQUALS_OPTION_0'
% 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: !p f. 'h4/const/option/OPTION_BIND' p f = 'h4/const/option/NONE' <=> p = 'h4/const/option/NONE' \/ (?x. p = 'h4/const/option/SOME' x /\ f x = 'h4/const/option/NONE')
%   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: !p f. 'h4/const/option/OPTION_BIND' p f = 'h4/const/option/NONE' <=> p = 'h4/const/option/NONE' \/ (?x. p = 'h4/const/option/SOME' x /\ happ f x = 'h4/const/option/NONE')
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_3f100407,V_3f100403]: ![F, G]: (![X]: s(V_3f100403,happ(s(fun(V_3f100407,V_3f100403),F),s(V_3f100407,X))) = s(V_3f100403,happ(s(fun(V_3f100407,V_3f100403),G),s(V_3f100407,X))) => s(fun(V_3f100407,V_3f100403),F) = s(fun(V_3f100407,V_3f100403),G))).
fof('h4/thm/option/OPTION_BIND_EQUALS_OPTION_0', conjecture, ![A,B]: ![P, F]: (s('h4/type/option/option'(B),'h4/const/option/OPTION_BIND'(s('h4/type/option/option'(A),P),s(fun(A,'h4/type/option/option'(B)),F))) = s('h4/type/option/option'(B),'h4/const/option/NONE') <=> (s('h4/type/option/option'(A),P) = s('h4/type/option/option'(A),'h4/const/option/NONE') | ?[X]: (s('h4/type/option/option'(A),P) = s('h4/type/option/option'(A),'h4/const/option/SOME'(s(A,X))) & s('h4/type/option/option'(B),happ(s(fun(A,'h4/type/option/option'(B)),F),s(A,X))) = s('h4/type/option/option'(B),'h4/const/option/NONE'))))).
