let i, n be Nat; :: thesis: ( i in Seg n implies i + 1 in Seg (n + 1) )
assume A1: i in Seg n ; :: thesis: i + 1 in Seg (n + 1)
then 1 <= i by FINSEQ_1:1;
then 1 + 1 <= i + 1 by XREAL_1:6;
then A2: 1 <= i + 1 by XXREAL_0:2;
i <= n by A1, FINSEQ_1:1;
then i + 1 <= n + 1 by XREAL_1:6;
hence i + 1 in Seg (n + 1) by A2, FINSEQ_1:1; :: thesis: verum