let f be V19() standard special_circular_sequence; :: thesis: ( f /. 1 = E-min (L~ f) & E-min (L~ f) <> S-max (L~ f) implies (E-min (L~ f)) .. f < (S-max (L~ f)) .. f )
assume that
A1: f /. 1 = E-min (L~ f) and
A2: E-min (L~ f) <> S-max (L~ f) ; :: thesis: (E-min (L~ f)) .. f < (S-max (L~ f)) .. f
A3: S-max (L~ f) in rng f by SPRECT_2:42;
then (S-max (L~ f)) .. f in dom f by FINSEQ_4:20;
then A4: (S-max (L~ f)) .. f >= 1 by FINSEQ_3:25;
( E-min (L~ f) in rng f & (E-min (L~ f)) .. f = 1 ) by A1, FINSEQ_6:43, SPRECT_2:45;
hence (E-min (L~ f)) .. f < (S-max (L~ f)) .. f by A3, A2, A4, FINSEQ_5:9, XXREAL_0:1; :: thesis: verum