let f be non constant standard special_circular_sequence; :: thesis: for i, j being Element of NAT st i < j & ( ( 1 < i & j <= len f ) or ( 1 <= i & j < len f ) ) holds
mid f,i,j is S-Sequence_in_R2
let i, j be Element of NAT ; :: thesis: ( i < j & ( ( 1 < i & j <= len f ) or ( 1 <= i & j < len f ) ) implies mid f,i,j is S-Sequence_in_R2 )
assume that
A1: i < j and
A2: ( ( 1 < i & j <= len f ) or ( 1 <= i & j < len f ) ) ; :: thesis: mid f,i,j is S-Sequence_in_R2
A3: Rev (Rev (mid f,i,j)) = mid f,i,j by FINSEQ_6:29;
mid f,j,i is S-Sequence_in_R2 by A1, A2, Th41;
then Rev (mid f,i,j) is S-Sequence_in_R2 by JORDAN4:30;
hence mid f,i,j is S-Sequence_in_R2 by A3, SPPOL_2:47; :: thesis: verum