%   ORIGINAL: 'h4/thm/option/OPTION_APPLY_o_'
% 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 g f. 'h4/const/option/OPTION_APPLY' ('h4/const/option/OPTION_APPLY' ('h4/const/option/OPTION_APPLY' ('h4/const/option/SOME' 'h4/const/combin/o') f) g) x = 'h4/const/option/OPTION_APPLY' f ('h4/const/option/OPTION_APPLY' g x)
%   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 g f. 'h4/const/option/OPTION_APPLY' ('h4/const/option/OPTION_APPLY' ('h4/const/option/OPTION_APPLY' ('h4/const/option/SOME' 'h4/const/combin/o') f) g) x = 'h4/const/option/OPTION_APPLY' f ('h4/const/option/OPTION_APPLY' g x)
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_3f100682,V_3f100678]: ![F, G]: (![X]: s(V_3f100678,happ(s(fun(V_3f100682,V_3f100678),F),s(V_3f100682,X))) = s(V_3f100678,happ(s(fun(V_3f100682,V_3f100678),G),s(V_3f100682,X))) => s(fun(V_3f100682,V_3f100678),F) = s(fun(V_3f100682,V_3f100678),G))).
fof('h4/thm/option/OPTION_APPLY_o_', conjecture, ![C,B,A]: ![X, G, F]: s('h4/type/option/option'(C),'h4/const/option/OPTION_APPLY'(s('h4/type/option/option'(fun(A,C)),'h4/const/option/OPTION_APPLY'(s('h4/type/option/option'(fun(fun(A,B),fun(A,C))),'h4/const/option/OPTION_APPLY'(s('h4/type/option/option'(fun(fun(B,C),fun(fun(A,B),fun(A,C)))),'h4/const/option/SOME'(s(fun(fun(B,C),fun(fun(A,B),fun(A,C))),'h4/const/combin/o'))),s('h4/type/option/option'(fun(B,C)),F))),s('h4/type/option/option'(fun(A,B)),G))),s('h4/type/option/option'(A),X))) = s('h4/type/option/option'(C),'h4/const/option/OPTION_APPLY'(s('h4/type/option/option'(fun(B,C)),F),s('h4/type/option/option'(B),'h4/const/option/OPTION_APPLY'(s('h4/type/option/option'(fun(A,B)),G),s('h4/type/option/option'(A),X)))))).
