thus not the carrier of (SCM R) is empty by Def1; :: according to STRUCT_0:def 1 :: thesis: SCM R is standard-ins
consider X being non empty set such that
A1: proj2 (SCM-Instr R) c= X * by FINSEQ_1:85;
take X ; :: according to COMPOS_1:def 4 :: thesis: the Instructions of (SCM R) c= [:NAT,(NAT *),(X *):]
A2: SCM-Instr R c= [:NAT,(NAT *),(proj2 (SCM-Instr R)):] by SCMRING1:17;
[:NAT,(NAT *),(proj2 (SCM-Instr R)):] c= [:NAT,(NAT *),(X *):] by A1, MCART_1:73;
then SCM-Instr R c= [:NAT,(NAT *),(X *):] by A2, XBOOLE_1:1;
hence the Instructions of (SCM R) c= [:NAT,(NAT *),(X *):] by Def1; :: thesis: verum