%   ORIGINAL: 'h4/thm/poly/POLY_ADD_CLAUSES_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: !t2 t1 h2 h1. 'h4/const/poly/poly_add' ('h4/const/list/CONS' h1 t1) ('h4/const/list/CONS' h2 t2) = 'h4/const/list/CONS' ('h4/const/realax/real_add' h1 h2) ('h4/const/poly/poly_add' t1 t2)
%   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: !t2 t1 h2 h1. 'h4/const/poly/poly_add' ('h4/const/list/CONS' h1 t1) ('h4/const/list/CONS' h2 t2) = 'h4/const/list/CONS' ('h4/const/realax/real_add' h1 h2) ('h4/const/poly/poly_add' t1 t2)
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_3f46034,V_3f46030]: ![F, G]: (![X]: s(V_3f46030,happ(s(fun(V_3f46034,V_3f46030),F),s(V_3f46034,X))) = s(V_3f46030,happ(s(fun(V_3f46034,V_3f46030),G),s(V_3f46034,X))) => s(fun(V_3f46034,V_3f46030),F) = s(fun(V_3f46034,V_3f46030),G))).
fof('h4/thm/poly/POLY_ADD_CLAUSES_e2', conjecture, ![T2, T1, H2, H1]: s('h4/type/list/list'('h4/type/realax/real'),'h4/const/poly/poly_add'(s('h4/type/list/list'('h4/type/realax/real'),'h4/const/list/CONS'(s('h4/type/realax/real',H1),s('h4/type/list/list'('h4/type/realax/real'),T1))),s('h4/type/list/list'('h4/type/realax/real'),'h4/const/list/CONS'(s('h4/type/realax/real',H2),s('h4/type/list/list'('h4/type/realax/real'),T2))))) = s('h4/type/list/list'('h4/type/realax/real'),'h4/const/list/CONS'(s('h4/type/realax/real','h4/const/realax/real_add'(s('h4/type/realax/real',H1),s('h4/type/realax/real',H2))),s('h4/type/list/list'('h4/type/realax/real'),'h4/const/poly/poly_add'(s('h4/type/list/list'('h4/type/realax/real'),T1),s('h4/type/list/list'('h4/type/realax/real'),T2)))))).
