%   ORIGINAL: 'h4/thm/list/LIST_REL_LENGTH_'
% 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 x y. 'h4/const/list/LIST_REL' R x y ==> 'h4/const/list/LENGTH' x = 'h4/const/list/LENGTH' y
%   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 x y. 'h4/const/list/LIST_REL' R x y ==> 'h4/const/list/LENGTH' x = 'h4/const/list/LENGTH' y
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_3f5939,V_3f5935]: ![F, G]: (![X]: s(V_3f5935,happ(s(fun(V_3f5939,V_3f5935),F),s(V_3f5939,X))) = s(V_3f5935,happ(s(fun(V_3f5939,V_3f5935),G),s(V_3f5939,X))) => s(fun(V_3f5939,V_3f5935),F) = s(fun(V_3f5939,V_3f5935),G))).
fof('h4/thm/list/LIST_REL_LENGTH_', conjecture, ![A,B]: ![R, X, Y]: (p(s(bool,'h4/const/list/LIST_REL'(s(fun(A,fun(B,bool)),R),s('h4/type/list/list'(A),X),s('h4/type/list/list'(B),Y)))) => s('h4/type/num/num','h4/const/list/LENGTH'(s('h4/type/list/list'(A),X))) = s('h4/type/num/num','h4/const/list/LENGTH'(s('h4/type/list/list'(B),Y))))).
