%   ORIGINAL: 'h4/thm/option/some_elim_'
% 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: !Q P. Q ('h4/const/option/some' P) ==> (?x. P x /\ Q ('h4/const/option/SOME' x)) \/ (!x. ~P x) /\ Q '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: !Q P. happ Q ('h4/const/option/some' P) ==> (?x. happ P x /\ happ Q ('h4/const/option/SOME' x)) \/ (!x. ~happ P x) /\ happ Q '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_3f100782,V_3f100778]: ![F, G]: (![X]: s(V_3f100778,happ(s(fun(V_3f100782,V_3f100778),F),s(V_3f100782,X))) = s(V_3f100778,happ(s(fun(V_3f100782,V_3f100778),G),s(V_3f100782,X))) => s(fun(V_3f100782,V_3f100778),F) = s(fun(V_3f100782,V_3f100778),G))).
fof('h4/thm/option/some_elim_', conjecture, ![A]: ![Q, P]: (p(s(bool,happ(s(fun('h4/type/option/option'(A),bool),Q),s('h4/type/option/option'(A),'h4/const/option/some'(s(fun(A,bool),P)))))) => (?[X]: (p(s(bool,happ(s(fun(A,bool),P),s(A,X)))) & p(s(bool,happ(s(fun('h4/type/option/option'(A),bool),Q),s('h4/type/option/option'(A),'h4/const/option/SOME'(s(A,X))))))) | (![X]: ~ (p(s(bool,happ(s(fun(A,bool),P),s(A,X))))) & p(s(bool,happ(s(fun('h4/type/option/option'(A),bool),Q),s('h4/type/option/option'(A),'h4/const/option/NONE')))))))).
