let a be natural Ordinal; :: thesis: ( a <> {} implies RED (a,a) = 1 )
assume A1: a <> {} ; :: thesis: RED (a,a) = 1
thus RED (a,a) = a div^ a by Th16
.= (a *^ 1) div^ a by ORDINAL2:39
.= 1 by A1, ORDINAL3:68 ; :: thesis: verum