let a, b, c, d be real number ; :: thesis: c ^2 <= (((a ^2) + (b ^2)) + (c ^2)) + (d ^2)
A1: 0 <= b ^2 by XREAL_1:65;
A2: 0 <= d ^2 by XREAL_1:65;
c ^2 <= (a ^2) + (c ^2) by XREAL_1:33, XREAL_1:65;
then 0 + (c ^2) <= ((a ^2) + (c ^2)) + (b ^2) by A1, XREAL_1:9;
hence c ^2 <= (((a ^2) + (b ^2)) + (c ^2)) + (d ^2) by A2, XREAL_1:9; :: thesis: verum