let i, j be Element of SCM-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 <= 8 by Th10;

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 = 7 or InsCode i = 8 or InsCode i = 6 ) by NAT_1:32;

suppose InsCode i = 0 ; :: thesis: dom (i `2_3) = dom (j `2_3)

then ( i in {[SCM-Halt,{},{}]} & j in {[SCM-Halt,{},{}]} ) by A1, Th9;
then ( i = [SCM-Halt,{},{}] & j = [SCM-Halt,{},{}] ) by TARSKI:def 1;
hence dom (i `2_3) = dom (j `2_3) ; :: thesis: verum

end;

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

then ( JumpPart i = {} & JumpPart j = {} ) by A1, Lm1;
hence dom (i `2_3) = dom (j `2_3) ; :: thesis: verum

end;

suppose ( InsCode i = 7 or InsCode i = 8 ) ; :: thesis: dom (i `2_3) = dom (j `2_3)

then ( dom (JumpPart i) = Seg 1 & dom (JumpPart j) = Seg 1 ) by A1, Lm2;
hence dom (i `2_3) = dom (j `2_3) ; :: thesis: verum

end;

suppose InsCode i = 6 ; :: thesis: dom (i `2_3) = dom (j `2_3)

then ( dom (JumpPart i) = Seg 1 & dom (JumpPart j) = Seg 1 ) by A1, Lm3;
hence dom (i `2_3) = dom (j `2_3) ; :: thesis: verum

end;

end;