let f be V8() standard special_circular_sequence; :: thesis: len (GoB f) > 1
A1: len (GoB f) <> 0 by MATRIX_0:def 10;
1 in dom f by FINSEQ_5:6;
then consider i2, j2 being Nat such that
A2: [i2,j2] in Indices (GoB f) and
A3: f /. 1 = (GoB f) * (i2,j2) by GOBOARD2:14;
A4: 1 <= i2 by A2, MATRIX_0:32;
assume len (GoB f) <= 1 ; :: thesis: contradiction
then A5: len (GoB f) = 1 by A1, NAT_1:25;
then i2 <= 1 by A2, MATRIX_0:32;
then A6: i2 = 1 by A4, XXREAL_0:1;
consider i being Nat such that
A7: i in dom f and
A8: (f /. i) `1 <> (f /. 1) `1 by Th30;
consider i1, j1 being Nat such that
A9: [i1,j1] in Indices (GoB f) and
A10: f /. i = (GoB f) * (i1,j1) by A7, GOBOARD2:14;
A11: ( 1 <= j1 & j1 <= width (GoB f) ) by A9, MATRIX_0:32;
A12: 1 <= i1 by A9, MATRIX_0:32;
i1 <= 1 by A5, A9, MATRIX_0:32;
then i1 = 1 by A12, XXREAL_0:1;
then A13: ((GoB f) * (i1,j1)) `1 = ((GoB f) * (1,1)) `1 by A5, A11, GOBOARD5:2;
( 1 <= j2 & j2 <= width (GoB f) ) by A2, MATRIX_0:32;
hence contradiction by A5, A8, A10, A3, A13, A6, GOBOARD5:2; :: thesis: verum