%   ORIGINAL: 'h4/thm/list/list_size_cong_'
% 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: !M N f 'f\''. M = N /\ (!x. 'h4/const/bool/IN' x ('h4/const/list/LIST_TO_SET' N) ==> f x = 'f\'' x) ==> 'h4/const/list/list_size' f M = 'h4/const/list/list_size' 'f\'' N
%   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: !M N f 'f\''. M = N /\ (!x. 'h4/const/bool/IN' x ('h4/const/list/LIST_TO_SET' N) ==> happ f x = happ 'f\'' x) ==> 'h4/const/list/list_size' f M = 'h4/const/list/list_size' 'f\'' N
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_3f5964,V_3f5960]: ![F, G]: (![X]: s(V_3f5960,happ(s(fun(V_3f5964,V_3f5960),F),s(V_3f5964,X))) = s(V_3f5960,happ(s(fun(V_3f5964,V_3f5960),G),s(V_3f5964,X))) => s(fun(V_3f5964,V_3f5960),F) = s(fun(V_3f5964,V_3f5960),G))).
fof('h4/thm/list/list_size_cong_', conjecture, ![A]: ![M, N, F, V_27f_5c_27_27]: ((s('h4/type/list/list'(A),M) = s('h4/type/list/list'(A),N) & ![X]: (p(s(bool,'h4/const/bool/IN'(s(A,X),s(fun(A,bool),'h4/const/list/LIST_TO_SET'(s('h4/type/list/list'(A),N)))))) => s('h4/type/num/num',happ(s(fun(A,'h4/type/num/num'),F),s(A,X))) = s('h4/type/num/num',happ(s(fun(A,'h4/type/num/num'),V_27f_5c_27_27),s(A,X))))) => s('h4/type/num/num','h4/const/list/list_size'(s(fun(A,'h4/type/num/num'),F),s('h4/type/list/list'(A),M))) = s('h4/type/num/num','h4/const/list/list_size'(s(fun(A,'h4/type/num/num'),V_27f_5c_27_27),s('h4/type/list/list'(A),N))))).
