let f be non constant standard special_circular_sequence; :: thesis: ( f /. 1 = W-max (L~ f) & W-max (L~ f) <> N-min (L~ f) implies (W-max (L~ f)) .. f < (N-min (L~ f)) .. f )
assume that
A1: f /. 1 = W-max (L~ f) and
A2: W-max (L~ f) <> N-min (L~ f) ; :: thesis: (W-max (L~ f)) .. f < (N-min (L~ f)) .. f
A3: N-min (L~ f) in rng f by SPRECT_2:43;
then (N-min (L~ f)) .. f in dom f by FINSEQ_4:30;
then A4: (N-min (L~ f)) .. f >= 1 by FINSEQ_3:27;
( W-max (L~ f) in rng f & (W-max (L~ f)) .. f = 1 ) by A1, FINSEQ_6:47, SPRECT_2:48;
hence (W-max (L~ f)) .. f < (N-min (L~ f)) .. f by A3, A2, A4, FINSEQ_5:10, XXREAL_0:1; :: thesis: verum