%   ORIGINAL: 'h4/thm/list/LENGTH_EQ_NUM_1'
% 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: !l n. 'h4/const/list/LENGTH' l = 'h4/const/num/SUC' n <=> (?h 'l\''. 'h4/const/list/LENGTH' 'l\'' = n /\ l = 'h4/const/list/CONS' h '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: !l n. 'h4/const/list/LENGTH' l = 'h4/const/num/SUC' n <=> (?h 'l\''. 'h4/const/list/LENGTH' 'l\'' = n /\ l = 'h4/const/list/CONS' h '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_3f4188,V_3f4184]: ![F, G]: (![X]: s(V_3f4184,happ(s(fun(V_3f4188,V_3f4184),F),s(V_3f4188,X))) = s(V_3f4184,happ(s(fun(V_3f4188,V_3f4184),G),s(V_3f4188,X))) => s(fun(V_3f4188,V_3f4184),F) = s(fun(V_3f4188,V_3f4184),G))).
fof('h4/thm/list/LENGTH_EQ_NUM_1', conjecture, ![A]: ![L, N]: (s('h4/type/num/num','h4/const/list/LENGTH'(s('h4/type/list/list'(A),L))) = s('h4/type/num/num','h4/const/num/SUC'(s('h4/type/num/num',N))) <=> ?[H, V_27l_5c_27_27]: (s('h4/type/num/num','h4/const/list/LENGTH'(s('h4/type/list/list'(A),V_27l_5c_27_27))) = s('h4/type/num/num',N) & s('h4/type/list/list'(A),L) = s('h4/type/list/list'(A),'h4/const/list/CONS'(s(A,H),s('h4/type/list/list'(A),V_27l_5c_27_27)))))).
