let z be V19() standard clockwise_oriented special_circular_sequence; ( z /. 1 = W-min (L~ z) implies (E-max (L~ z)) .. z < (E-min (L~ z)) .. z )
set g = Rotate (z,(N-min (L~ z)));
A1:
L~ z = L~ (Rotate (z,(N-min (L~ z))))
by REVROT_1:33;
N-min (L~ z) in rng z
by SPRECT_2:39;
then
(Rotate (z,(N-min (L~ z)))) /. 1 = N-min (L~ (Rotate (z,(N-min (L~ z)))))
by A1, FINSEQ_6:92;
then A2:
( (E-max (L~ (Rotate (z,(N-min (L~ z)))))) .. (Rotate (z,(N-min (L~ z)))) < (E-min (L~ (Rotate (z,(N-min (L~ z)))))) .. (Rotate (z,(N-min (L~ z)))) & (E-min (L~ (Rotate (z,(N-min (L~ z)))))) .. (Rotate (z,(N-min (L~ z)))) < (W-min (L~ (Rotate (z,(N-min (L~ z)))))) .. (Rotate (z,(N-min (L~ z)))) )
by Lm5, SPRECT_2:71;
A3:
W-min (L~ (Rotate (z,(N-min (L~ z))))) in rng (Rotate (z,(N-min (L~ z))))
by SPRECT_2:43;
assume A4:
z /. 1 = W-min (L~ z)
; (E-max (L~ z)) .. z < (E-min (L~ z)) .. z
for i being Nat st 1 < i & i < len z holds
z /. i <> z /. 1
by GOBOARD7:36;
then A5:
Rotate ((Rotate (z,(N-min (L~ z)))),(W-min (L~ z))) = z
by A4, FINSEQ_6:181;
( E-min (L~ (Rotate (z,(N-min (L~ z))))) in rng (Rotate (z,(N-min (L~ z)))) & E-max (L~ (Rotate (z,(N-min (L~ z))))) in rng (Rotate (z,(N-min (L~ z)))) )
by SPRECT_2:45, SPRECT_2:46;
hence
(E-max (L~ z)) .. z < (E-min (L~ z)) .. z
by A1, A5, A3, A2, Th11; verum