let i, j be Element of SCM+FSA-Instr ; :: according to COMPOS_0:def 5 :: thesis: ( not InsCode i = InsCode j or dom (i `2_3) = dom (j `2_3) )
assume A1: InsCode i = InsCode j ; :: thesis: dom (i `2_3) = dom (j `2_3)
InsCode i <= 12 by Lm2;

per cases then ( InsCode i = 0 or InsCode i = 1 or InsCode i = 2 or InsCode i = 3 or InsCode i = 4 or InsCode i = 5 or InsCode i = 6 or InsCode i = 7 or InsCode i = 8 or InsCode i = 9 or InsCode i = 10 or InsCode i = 11 or InsCode i = 12 ) by NAT_1:36;

suppose ( InsCode i = 0 or InsCode i = 1 or InsCode i = 2 or InsCode i = 3 or InsCode i = 4 or InsCode i = 5 or InsCode i = 6 or InsCode i = 7 or InsCode i = 8 ) ; :: thesis: dom (i `2_3) = dom (j `2_3)

then ( i in SCM-Instr & j in SCM-Instr ) by A1, Th7;
hence dom (i `2_3) = dom (j `2_3) by A1, COMPOS_0:def 5; :: thesis: verum

end;

suppose ( InsCode i = 9 or InsCode i = 10 ) ; :: thesis: dom (i `2_3) = dom (j `2_3)

then ( JumpPart i = {} & JumpPart j = {} ) by A1, Lm3;
hence dom (i `2_3) = dom (j `2_3) ; :: thesis: verum

end;

suppose ( InsCode i = 11 or InsCode i = 12 ) ; :: thesis: dom (i `2_3) = dom (j `2_3)

then ( JumpPart i = {} & JumpPart j = {} ) by A1, Lm4;
hence dom (i `2_3) = dom (j `2_3) ; :: thesis: verum

end;

end;