%   ORIGINAL: 'h4/thm/list/ALL_DISTINCT_CARD_LIST_TO_SET_'
% 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: !ls. 'h4/const/list/ALL_DISTINCT' ls ==> 'h4/const/pred_set/CARD' ('h4/const/list/LIST_TO_SET' ls) = 'h4/const/list/LENGTH' ls
%   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: !ls. 'h4/const/list/ALL_DISTINCT' ls ==> 'h4/const/pred_set/CARD' ('h4/const/list/LIST_TO_SET' ls) = 'h4/const/list/LENGTH' ls
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_3f8165,V_3f8161]: ![F, G]: (![X]: s(V_3f8161,happ(s(fun(V_3f8165,V_3f8161),F),s(V_3f8165,X))) = s(V_3f8161,happ(s(fun(V_3f8165,V_3f8161),G),s(V_3f8165,X))) => s(fun(V_3f8165,V_3f8161),F) = s(fun(V_3f8165,V_3f8161),G))).
fof('h4/thm/list/ALL_DISTINCT_CARD_LIST_TO_SET_', conjecture, ![A]: ![Ls]: (p(s(bool,'h4/const/list/ALL_DISTINCT'(s('h4/type/list/list'(A),Ls)))) => s('h4/type/num/num','h4/const/pred_set/CARD'(s(fun(A,bool),'h4/const/list/LIST_TO_SET'(s('h4/type/list/list'(A),Ls))))) = s('h4/type/num/num','h4/const/list/LENGTH'(s('h4/type/list/list'(A),Ls))))).
