let k, m be Nat; ( 2 <= k & m is_represented_by 1,k implies DigA_SDSub (SD2SDSub (DecSD m,1,k)),(1 + 1) = SDSub_Add_Carry m,k )
assume that
A1:
2 <= k
and
A2:
m is_represented_by 1,k
; DigA_SDSub (SD2SDSub (DecSD m,1,k)),(1 + 1) = SDSub_Add_Carry m,k
thus DigA_SDSub (SD2SDSub (DecSD m,1,k)),(1 + 1) =
SDSub_Add_Carry (DigA (DecSD m,1,k),1),k
by A1, Th3
.=
SDSub_Add_Carry m,k
by A2, RADIX_1:24
; verum