%   ORIGINAL: 'h4/thm/rich_list/UNZIP_SNOC_'
% 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 l. 'h4/const/list/UNZIP' ('h4/const/list/SNOC' x l) = 'h4/const/pair/,' ('h4/const/list/SNOC' ('h4/const/pair/FST' x) ('h4/const/pair/FST' ('h4/const/list/UNZIP' l))) ('h4/const/list/SNOC' ('h4/const/pair/SND' x) ('h4/const/pair/SND' ('h4/const/list/UNZIP' l)))
%   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 l. 'h4/const/list/UNZIP' ('h4/const/list/SNOC' x l) = 'h4/const/pair/,' ('h4/const/list/SNOC' ('h4/const/pair/FST' x) ('h4/const/pair/FST' ('h4/const/list/UNZIP' l))) ('h4/const/list/SNOC' ('h4/const/pair/SND' x) ('h4/const/pair/SND' ('h4/const/list/UNZIP' l)))
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_3f55786,V_3f55782]: ![F, G]: (![X]: s(V_3f55782,happ(s(fun(V_3f55786,V_3f55782),F),s(V_3f55786,X))) = s(V_3f55782,happ(s(fun(V_3f55786,V_3f55782),G),s(V_3f55786,X))) => s(fun(V_3f55786,V_3f55782),F) = s(fun(V_3f55786,V_3f55782),G))).
fof('h4/thm/rich_list/UNZIP_SNOC_', conjecture, ![A,B]: ![X, L]: s('h4/type/pair/prod'('h4/type/list/list'(A),'h4/type/list/list'(B)),'h4/const/list/UNZIP'(s('h4/type/list/list'('h4/type/pair/prod'(A,B)),'h4/const/list/SNOC'(s('h4/type/pair/prod'(A,B),X),s('h4/type/list/list'('h4/type/pair/prod'(A,B)),L))))) = s('h4/type/pair/prod'('h4/type/list/list'(A),'h4/type/list/list'(B)),'h4/const/pair/,'(s('h4/type/list/list'(A),'h4/const/list/SNOC'(s(A,'h4/const/pair/FST'(s('h4/type/pair/prod'(A,B),X))),s('h4/type/list/list'(A),'h4/const/pair/FST'(s('h4/type/pair/prod'('h4/type/list/list'(A),'h4/type/list/list'(B)),'h4/const/list/UNZIP'(s('h4/type/list/list'('h4/type/pair/prod'(A,B)),L))))))),s('h4/type/list/list'(B),'h4/const/list/SNOC'(s(B,'h4/const/pair/SND'(s('h4/type/pair/prod'(A,B),X))),s('h4/type/list/list'(B),'h4/const/pair/SND'(s('h4/type/pair/prod'('h4/type/list/list'(A),'h4/type/list/list'(B)),'h4/const/list/UNZIP'(s('h4/type/list/list'('h4/type/pair/prod'(A,B)),L)))))))))).
