let f be non constant standard special_circular_sequence; :: thesis: len (GoB f) > 1
assume A1:
len (GoB f) <= 1
; :: thesis: contradiction
len (GoB f) <> 0
by GOBOARD1:def 5;
then A2:
len (GoB f) = 1
by A1, NAT_1:26;
consider i being Element of NAT such that
A3:
i in dom f
and
A4:
(f /. i) `1 <> (f /. 1) `1
by Th32;
consider i1, j1 being Element of NAT such that
A5:
[i1,j1] in Indices (GoB f)
and
A6:
f /. i = (GoB f) * i1,j1
by A3, GOBOARD2:25;
1 in dom f
by FINSEQ_5:6;
then consider i2, j2 being Element of NAT such that
A7:
[i2,j2] in Indices (GoB f)
and
A8:
f /. 1 = (GoB f) * i2,j2
by GOBOARD2:25;
A9:
( 1 <= j1 & j1 <= width (GoB f) )
by A5, MATRIX_1:39;
A10:
( 1 <= j2 & j2 <= width (GoB f) )
by A7, MATRIX_1:39;
( 1 <= i1 & i1 <= 1 )
by A2, A5, MATRIX_1:39;
then
i1 = 1
by XXREAL_0:1;
then A11:
((GoB f) * i1,j1) `1 = ((GoB f) * 1,1) `1
by A2, A9, GOBOARD5:3;
( 1 <= i2 & i2 <= 1 )
by A2, A7, MATRIX_1:39;
then
i2 = 1
by XXREAL_0:1;
hence
contradiction
by A2, A4, A6, A8, A10, A11, GOBOARD5:3; :: thesis: verum