:: deftheorem defines is_Standard_Representation_of GROEB_2:def 7 :
for n being Ordinal
for T being connected TermOrder of n
for L being non empty non trivial right_complementable well-unital distributive add-associative right_zeroed doubleLoopStr
for f being Polynomial of n,L
for P being non empty Subset of (Polynom-Ring (n,L))
for A being LeftLinearCombination of P
for b being bag of n holds
( A is_Standard_Representation_of f,P,b,T iff ( Sum A = f & ( for i being Element of NAT st i in dom A holds
ex m being non-zero Monomial of n,L ex p being non-zero Polynomial of n,L st
( p in P & A /. i = m *' p & HT ((m *' p),T) <= b,T ) ) ) );