%   ORIGINAL: 'h4/thm/poly/POLY_MUL_'
% 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: !x p1 p2. 'h4/const/poly/poly' ('h4/const/poly/poly_mul' p1 p2) x = 'h4/const/realax/real_mul' ('h4/const/poly/poly' p1 x) ('h4/const/poly/poly' p2 x)
%   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: !x p1 p2. 'h4/const/poly/poly' ('h4/const/poly/poly_mul' p1 p2) x = 'h4/const/realax/real_mul' ('h4/const/poly/poly' p1 x) ('h4/const/poly/poly' p2 x)
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_3f46384,V_3f46380]: ![F, G]: (![X]: s(V_3f46380,happ(s(fun(V_3f46384,V_3f46380),F),s(V_3f46384,X))) = s(V_3f46380,happ(s(fun(V_3f46384,V_3f46380),G),s(V_3f46384,X))) => s(fun(V_3f46384,V_3f46380),F) = s(fun(V_3f46384,V_3f46380),G))).
fof('h4/thm/poly/POLY_MUL_', conjecture, ![X, P1, P2]: s('h4/type/realax/real','h4/const/poly/poly'(s('h4/type/list/list'('h4/type/realax/real'),'h4/const/poly/poly_mul'(s('h4/type/list/list'('h4/type/realax/real'),P1),s('h4/type/list/list'('h4/type/realax/real'),P2))),s('h4/type/realax/real',X))) = s('h4/type/realax/real','h4/const/realax/real_mul'(s('h4/type/realax/real','h4/const/poly/poly'(s('h4/type/list/list'('h4/type/realax/real'),P1),s('h4/type/realax/real',X))),s('h4/type/realax/real','h4/const/poly/poly'(s('h4/type/list/list'('h4/type/realax/real'),P2),s('h4/type/realax/real',X)))))).
