let f be non trivial special unfolded standard FinSequence of (TOP-REAL 2); :: thesis: ( ( ( f /. 1 <> N-min (L~ f) & f /. (len f) <> N-min (L~ f) ) or ( f /. 1 <> N-max (L~ f) & f /. (len f) <> N-max (L~ f) ) ) implies N-min (L~ f) <> N-max (L~ f) )

assume ( ( f /. 1 <> N-min (L~ f) & f /. (len f) <> N-min (L~ f) ) or ( f /. 1 <> N-max (L~ f) & f /. (len f) <> N-max (L~ f) ) ) ; :: thesis: N-min (L~ f) <> N-max (L~ f)

then (N-min (L~ f)) `1 < (N-max (L~ f)) `1 by Th8;

hence N-min (L~ f) <> N-max (L~ f) ; :: thesis: verum

assume ( ( f /. 1 <> N-min (L~ f) & f /. (len f) <> N-min (L~ f) ) or ( f /. 1 <> N-max (L~ f) & f /. (len f) <> N-max (L~ f) ) ) ; :: thesis: N-min (L~ f) <> N-max (L~ f)

then (N-min (L~ f)) `1 < (N-max (L~ f)) `1 by Th8;

hence N-min (L~ f) <> N-max (L~ f) ; :: thesis: verum