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