%   ORIGINAL: 'h4/thm/quotient_option/SOME_PRS_'
% 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: !R abs rep. 'h4/const/quotient/QUOTIENT' R abs rep ==> (!x. 'h4/const/option/SOME' x = 'h4/const/option/OPTION_MAP' abs ('h4/const/option/SOME' (rep 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: !R abs rep. 'h4/const/quotient/QUOTIENT' R abs rep ==> (!x. 'h4/const/option/SOME' x = 'h4/const/option/OPTION_MAP' abs ('h4/const/option/SOME' (happ rep 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_3f63536,V_3f63532]: ![F, G]: (![X]: s(V_3f63532,happ(s(fun(V_3f63536,V_3f63532),F),s(V_3f63536,X))) = s(V_3f63532,happ(s(fun(V_3f63536,V_3f63532),G),s(V_3f63536,X))) => s(fun(V_3f63536,V_3f63532),F) = s(fun(V_3f63536,V_3f63532),G))).
fof('h4/thm/quotient_option/SOME_PRS_', conjecture, ![A,B]: ![R, Abs, Rep]: (p(s(bool,'h4/const/quotient/QUOTIENT'(s(fun(A,fun(A,bool)),R),s(fun(A,B),Abs),s(fun(B,A),Rep)))) => ![X]: s('h4/type/option/option'(B),'h4/const/option/SOME'(s(B,X))) = s('h4/type/option/option'(B),'h4/const/option/OPTION_MAP'(s(fun(A,B),Abs),s('h4/type/option/option'(A),'h4/const/option/SOME'(s(A,happ(s(fun(B,A),Rep),s(B,X))))))))).
