let f be non trivial special unfolded standard FinSequence of (TOP-REAL 2); :: thesis: ( ( ( f /. 1 <> E-min (L~ f) & f /. (len f) <> E-min (L~ f) ) or ( f /. 1 <> E-max (L~ f) & f /. (len f) <> E-max (L~ f) ) ) implies E-min (L~ f) <> E-max (L~ f) )
assume ( ( f /. 1 <> E-min (L~ f) & f /. (len f) <> E-min (L~ f) ) or ( f /. 1 <> E-max (L~ f) & f /. (len f) <> E-max (L~ f) ) ) ; :: thesis: E-min (L~ f) <> E-max (L~ f)
then (E-min (L~ f)) `2 < (E-max (L~ f)) `2 by Th22;
hence E-min (L~ f) <> E-max (L~ f) ; :: thesis: verum