%   ORIGINAL: 'h4/thm/option/OPTION_MAP_EQ_NONE_both_ways_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: !x f. 'h4/const/option/OPTION_MAP' f x = 'h4/const/option/NONE' <=> 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: !x f. 'h4/const/option/OPTION_MAP' f x = 'h4/const/option/NONE' <=> 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_3f100182,V_3f100178]: ![F, G]: (![X]: s(V_3f100178,happ(s(fun(V_3f100182,V_3f100178),F),s(V_3f100182,X))) = s(V_3f100178,happ(s(fun(V_3f100182,V_3f100178),G),s(V_3f100182,X))) => s(fun(V_3f100182,V_3f100178),F) = s(fun(V_3f100182,V_3f100178),G))).
fof('h4/thm/option/OPTION_MAP_EQ_NONE_both_ways_0', conjecture, ![A,B]: ![X, F]: (s('h4/type/option/option'(A),'h4/const/option/OPTION_MAP'(s(fun(B,A),F),s('h4/type/option/option'(B),X))) = s('h4/type/option/option'(A),'h4/const/option/NONE') <=> s('h4/type/option/option'(B),X) = s('h4/type/option/option'(B),'h4/const/option/NONE'))).
