%   ORIGINAL: 'h4/thm/list/LENGTH_EQ_NUM_e2'
% 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 n1 n2. 'h4/const/list/LENGTH' l = 'h4/const/arithmetic/+' n1 n2 <=> (?l1 l2. 'h4/const/list/LENGTH' l1 = n1 /\ 'h4/const/list/LENGTH' l2 = n2 /\ l = 'h4/const/list/APPEND' l1 l2)
%   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 n1 n2. 'h4/const/list/LENGTH' l = 'h4/const/arithmetic/+' n1 n2 <=> (?l1 l2. 'h4/const/list/LENGTH' l1 = n1 /\ 'h4/const/list/LENGTH' l2 = n2 /\ l = 'h4/const/list/APPEND' l1 l2)
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_3f4213,V_3f4209]: ![F, G]: (![X]: s(V_3f4209,happ(s(fun(V_3f4213,V_3f4209),F),s(V_3f4213,X))) = s(V_3f4209,happ(s(fun(V_3f4213,V_3f4209),G),s(V_3f4213,X))) => s(fun(V_3f4213,V_3f4209),F) = s(fun(V_3f4213,V_3f4209),G))).
fof('h4/thm/list/LENGTH_EQ_NUM_e2', conjecture, ![A]: ![L, N1, N2]: (s('h4/type/num/num','h4/const/list/LENGTH'(s('h4/type/list/list'(A),L))) = s('h4/type/num/num','h4/const/arithmetic/+'(s('h4/type/num/num',N1),s('h4/type/num/num',N2))) <=> ?[L1, L2]: (s('h4/type/num/num','h4/const/list/LENGTH'(s('h4/type/list/list'(A),L1))) = s('h4/type/num/num',N1) & (s('h4/type/num/num','h4/const/list/LENGTH'(s('h4/type/list/list'(A),L2))) = s('h4/type/num/num',N2) & s('h4/type/list/list'(A),L) = s('h4/type/list/list'(A),'h4/const/list/APPEND'(s('h4/type/list/list'(A),L1),s('h4/type/list/list'(A),L2))))))).
