let n be Ordinal; :: thesis: for O being connected TermOrder of n
for L being non empty ZeroStr
for p being Polynomial of n,L holds
( HC p,O = 0. L iff p = 0_ n,L )
let O be connected TermOrder of n; :: thesis: for L being non empty ZeroStr
for p being Polynomial of n,L holds
( HC p,O = 0. L iff p = 0_ n,L )
let L be non empty ZeroStr ; :: thesis: for p being Polynomial of n,L holds
( HC p,O = 0. L iff p = 0_ n,L )
let p be Polynomial of n,L; :: thesis: ( HC p,O = 0. L iff p = 0_ n,L )

now

assume HC p,O = 0. L ; :: thesis: p = 0_ n,L
then not HT p,O in Support p by POLYNOM1:def 9;
then Support p = {} by Def6;
hence p = 0_ n,L by POLYNOM7:1; :: thesis: verum

end;

hence ( HC p,O = 0. L iff p = 0_ n,L ) by POLYNOM1:81; :: thesis: verum