%   ORIGINAL: 'h4/thm/option/OPTION_JOIN_EQ_SOME_'
% 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 y. 'h4/const/option/OPTION_JOIN' x = 'h4/const/option/SOME' y <=> x = 'h4/const/option/SOME' ('h4/const/option/SOME' y)
%   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 y. 'h4/const/option/OPTION_JOIN' x = 'h4/const/option/SOME' y <=> x = 'h4/const/option/SOME' ('h4/const/option/SOME' y)
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_3f100282,V_3f100278]: ![F, G]: (![X]: s(V_3f100278,happ(s(fun(V_3f100282,V_3f100278),F),s(V_3f100282,X))) = s(V_3f100278,happ(s(fun(V_3f100282,V_3f100278),G),s(V_3f100282,X))) => s(fun(V_3f100282,V_3f100278),F) = s(fun(V_3f100282,V_3f100278),G))).
fof('h4/thm/option/OPTION_JOIN_EQ_SOME_', conjecture, ![A]: ![X, Y]: (s('h4/type/option/option'(A),'h4/const/option/OPTION_JOIN'(s('h4/type/option/option'('h4/type/option/option'(A)),X))) = s('h4/type/option/option'(A),'h4/const/option/SOME'(s(A,Y))) <=> s('h4/type/option/option'('h4/type/option/option'(A)),X) = s('h4/type/option/option'('h4/type/option/option'(A)),'h4/const/option/SOME'(s('h4/type/option/option'(A),'h4/const/option/SOME'(s(A,Y))))))).
