let f be non constant standard special_circular_sequence; :: thesis: ( f /. 1 = W-min (L~ f) implies (W-min (L~ f)) .. f < (W-max (L~ f)) .. f )
A1: W-min (L~ f) in rng f by SPRECT_2:47;
A2: W-max (L~ f) in rng f by SPRECT_2:48;
then A3: (W-min (L~ f)) .. f <> (W-max (L~ f)) .. f by A1, FINSEQ_5:10, SPRECT_2:62;
(W-max (L~ f)) .. f in dom f by A2, FINSEQ_4:30;
then A4: (W-max (L~ f)) .. f >= 1 by FINSEQ_3:27;
assume f /. 1 = W-min (L~ f) ; :: thesis: (W-min (L~ f)) .. f < (W-max (L~ f)) .. f
then (W-min (L~ f)) .. f = 1 by FINSEQ_6:47;
hence (W-min (L~ f)) .. f < (W-max (L~ f)) .. f by A3, A4, XXREAL_0:1; :: thesis: verum