let f be constant standard special_circular_sequence; :: thesis: ( f /. 1 = W-min (L~ f) implies (W-min (L~ f)) .. f < (W-max (L~ f)) .. f )
assume f /. 1 = W-min (L~ f) ; :: thesis: (W-min (L~ f)) .. f < (W-max (L~ f)) .. f
then A1: (W-min (L~ f)) .. f = 1 by FINSEQ_6:43;
A2: W-max (L~ f) in rng f by SPRECT_2:44;
then (W-max (L~ f)) .. f in dom f by FINSEQ_4:20;
then A3: (W-max (L~ f)) .. f >= 1 by FINSEQ_3:25;
W-min (L~ f) in rng f by SPRECT_2:43;
then (W-min (L~ f)) .. f <> (W-max (L~ f)) .. f by A2, FINSEQ_5:9, SPRECT_2:58;
hence (W-min (L~ f)) .. f < (W-max (L~ f)) .. f by A3, A1, XXREAL_0:1; :: thesis: verum