%   ORIGINAL: 'h4/thm/poly/POLY_MUL_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: !t1 p2 k1 h1. 'h4/const/poly/poly_mul' ('h4/const/list/CONS' h1 ('h4/const/list/CONS' k1 t1)) p2 = 'h4/const/poly/poly_add' ('h4/const/poly/#hash##hash#' h1 p2) ('h4/const/list/CONS' ('h4/const/real/real_of_num' 'h4/const/num/0') ('h4/const/poly/poly_mul' ('h4/const/list/CONS' k1 t1) p2))
%   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: !t1 p2 k1 h1. 'h4/const/poly/poly_mul' ('h4/const/list/CONS' h1 ('h4/const/list/CONS' k1 t1)) p2 = 'h4/const/poly/poly_add' ('h4/const/poly/#hash##hash#' h1 p2) ('h4/const/list/CONS' ('h4/const/real/real_of_num' 'h4/const/num/0') ('h4/const/poly/poly_mul' ('h4/const/list/CONS' k1 t1) p2))
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_3f46209,V_3f46205]: ![F, G]: (![X]: s(V_3f46205,happ(s(fun(V_3f46209,V_3f46205),F),s(V_3f46209,X))) = s(V_3f46205,happ(s(fun(V_3f46209,V_3f46205),G),s(V_3f46209,X))) => s(fun(V_3f46209,V_3f46205),F) = s(fun(V_3f46209,V_3f46205),G))).
fof('h4/thm/poly/POLY_MUL_CLAUSES_e2', conjecture, ![T1, P2, K1, H1]: s('h4/type/list/list'('h4/type/realax/real'),'h4/const/poly/poly_mul'(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'),'h4/const/list/CONS'(s('h4/type/realax/real',K1),s('h4/type/list/list'('h4/type/realax/real'),T1))))),s('h4/type/list/list'('h4/type/realax/real'),P2))) = 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/poly/#hash##hash#'(s('h4/type/realax/real',H1),s('h4/type/list/list'('h4/type/realax/real'),P2))),s('h4/type/list/list'('h4/type/realax/real'),'h4/const/list/CONS'(s('h4/type/realax/real','h4/const/real/real_of_num'(s('h4/type/num/num','h4/const/num/0'))),s('h4/type/list/list'('h4/type/realax/real'),'h4/const/poly/poly_mul'(s('h4/type/list/list'('h4/type/realax/real'),'h4/const/list/CONS'(s('h4/type/realax/real',K1),s('h4/type/list/list'('h4/type/realax/real'),T1))),s('h4/type/list/list'('h4/type/realax/real'),P2)))))))).
