let n be Ordinal; :: thesis: for T being connected TermOrder of n
for L being non empty right_complementable add-associative right_zeroed addLoopStr
for p being Polynomial of n,L holds
( Upper_Support (p,T,(card (Support p))) = Support p & Lower_Support (p,T,(card (Support p))) = {} )
let T be connected TermOrder of n; :: thesis: for L being non empty right_complementable add-associative right_zeroed addLoopStr
for p being Polynomial of n,L holds
( Upper_Support (p,T,(card (Support p))) = Support p & Lower_Support (p,T,(card (Support p))) = {} )
let L be non empty right_complementable add-associative right_zeroed addLoopStr ; :: thesis: for p being Polynomial of n,L holds
( Upper_Support (p,T,(card (Support p))) = Support p & Lower_Support (p,T,(card (Support p))) = {} )
let p be Polynomial of n,L; :: thesis: ( Upper_Support (p,T,(card (Support p))) = Support p & Lower_Support (p,T,(card (Support p))) = {} )
set u = Upper_Support (p,T,(card (Support p)));
( Upper_Support (p,T,(card (Support p))) c= Support p & card (Upper_Support (p,T,(card (Support p)))) = card (Support p) ) by Def2;
hence Upper_Support (p,T,(card (Support p))) = Support p by CARD_2:102; :: thesis: Lower_Support (p,T,(card (Support p))) = {}
hence Lower_Support (p,T,(card (Support p))) = {} by XBOOLE_1:37; :: thesis: verum