let m, k be Nat; :: thesis: for r being Tuple of m + 2,k -SD st m >= 1 & k >= 2 holds
(SDDec (M0 r)) + (SDDec (DecSD 0 ,(m + 2),k)) = (SDDec (Mmin r)) + (SDDec (SDMax (m + 2),m,k))
let r be Tuple of m + 2,k -SD ; :: thesis: ( m >= 1 & k >= 2 implies (SDDec (M0 r)) + (SDDec (DecSD 0 ,(m + 2),k)) = (SDDec (Mmin r)) + (SDDec (SDMax (m + 2),m,k)) )
assume that
A1: m >= 1 and
A2: k >= 2 ; :: thesis: (SDDec (M0 r)) + (SDDec (DecSD 0 ,(m + 2),k)) = (SDDec (Mmin r)) + (SDDec (SDMax (m + 2),m,k))
A3: m + 2 > 1 by A1, Lm1;
(SDDec (M0 r)) + (SDDec (SDMin (m + 2),m,k)) = (SDDec (Mmin r)) + (SDDec (DecSD 0 ,(m + 2),k)) by A2, Th11
.= (SDDec (Mmin r)) + 0 by A3, RADIX_5:6 ;
then (SDDec (Mmin r)) + (SDDec (SDMax (m + 2),m,k)) = (SDDec (M0 r)) + ((SDDec (SDMax (m + 2),m,k)) + (SDDec (SDMin (m + 2),m,k)))
.= (SDDec (M0 r)) + (SDDec (DecSD 0 ,(m + 2),k)) by A2, A3, RADIX_5:17 ;
hence (SDDec (M0 r)) + (SDDec (DecSD 0 ,(m + 2),k)) = (SDDec (Mmin r)) + (SDDec (SDMax (m + 2),m,k)) ; :: thesis: verum