%   ORIGINAL: 'h4/thm/option/some_EQ_e1'
% 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: !y. 'h4/const/option/some' (\x. y = x) = '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: !_0. (!y x. happ (happ _0 y) x <=> y = x) ==> (!y. 'h4/const/option/some' (happ _0 y) = '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_3f100857,V_3f100853]: ![F, G]: (![X]: s(V_3f100853,happ(s(fun(V_3f100857,V_3f100853),F),s(V_3f100857,X))) = s(V_3f100853,happ(s(fun(V_3f100857,V_3f100853),G),s(V_3f100857,X))) => s(fun(V_3f100857,V_3f100853),F) = s(fun(V_3f100857,V_3f100853),G))).
fof('h4/thm/option/some_EQ_e1', conjecture, ![A]: ![V__0]: (![Y, X]: (p(s(bool,happ(s(fun(A,bool),happ(s(fun(A,fun(A,bool)),V__0),s(A,Y))),s(A,X)))) <=> s(A,Y) = s(A,X)) => ![Y]: s('h4/type/option/option'(A),'h4/const/option/some'(s(fun(A,bool),happ(s(fun(A,fun(A,bool)),V__0),s(A,Y))))) = s('h4/type/option/option'(A),'h4/const/option/SOME'(s(A,Y))))).
