let f be V19() standard special_circular_sequence; :: thesis: ( f /. 1 = E-max (L~ f) implies (E-max (L~ f)) .. f < (E-min (L~ f)) .. f )
assume f /. 1 = E-max (L~ f) ; :: thesis: (E-max (L~ f)) .. f < (E-min (L~ f)) .. f
then A1: (E-max (L~ f)) .. f = 1 by FINSEQ_6:43;
A2: E-min (L~ f) in rng f by SPRECT_2:45;
then (E-min (L~ f)) .. f in dom f by FINSEQ_4:20;
then A3: (E-min (L~ f)) .. f >= 1 by FINSEQ_3:25;
E-max (L~ f) in rng f by SPRECT_2:46;
then (E-min (L~ f)) .. f <> (E-max (L~ f)) .. f by A2, FINSEQ_5:9, SPRECT_2:54;
hence (E-max (L~ f)) .. f < (E-min (L~ f)) .. f by A3, A1, XXREAL_0:1; :: thesis: verum