let h be non constant standard special_circular_sequence; :: thesis: for i being Element of NAT st 1 <= i & i <= len h holds
( S-bound (L~ h) <= (h /. i) `2 & (h /. i) `2 <= N-bound (L~ h) )
let i be Element of NAT ; :: thesis: ( 1 <= i & i <= len h implies ( S-bound (L~ h) <= (h /. i) `2 & (h /. i) `2 <= N-bound (L~ h) ) )
A1: len h > 4 by GOBOARD7:34;
assume that
A2: 1 <= i and
A3: i <= len h ; :: thesis: ( S-bound (L~ h) <= (h /. i) `2 & (h /. i) `2 <= N-bound (L~ h) )
i in dom h by A2, A3, FINSEQ_3:25;
then h /. i in L~ h by A1, GOBOARD1:1, XXREAL_0:2;
hence ( S-bound (L~ h) <= (h /. i) `2 & (h /. i) `2 <= N-bound (L~ h) ) by PSCOMP_1:24; :: thesis: verum