let ins be Instruction of SCM; ( InsCode ins = 2 implies ex da, db being Data-Location st ins = AddTo (da,db) )
assume A1:
InsCode ins = 2
; ex da, db being Data-Location st ins = AddTo (da,db)
A3:
now not ins in { [K,<*a1*>,<*b1*>] where K is Element of Segm 9, a1 is Nat, b1 is Element of Data-Locations : K in {7,8} } assume
ins in { [K,<*a1*>,<*b1*>] where K is Element of Segm 9, a1 is Nat, b1 is Element of Data-Locations : K in {7,8} }
;
contradictionthen consider K being
Element of
Segm 9,
a1 being
Nat,
b1 being
Element of
Data-Locations such that A4:
ins = [K,<*a1*>,<*b1*>]
and A5:
K in {7,8}
;
InsCode ins = K
by A4;
hence
contradiction
by A1, A5, TARSKI:def 2;
verum end;
InsCode (halt SCM) = 0
by COMPOS_1:70;
then
not ins in {[SCM-Halt,{},{}]}
by A1, AMI_3:26, TARSKI:def 1;
then
not ins in {[SCM-Halt,{},{}]} \/ { [J,<*a*>,{}] where J is Element of Segm 9, a is Nat : J = 6 }
by A2, XBOOLE_0:def 3;
then
not ins in ({[SCM-Halt,{},{}]} \/ { [J,<*a*>,{}] where J is Element of Segm 9, a is Nat : J = 6 } ) \/ { [K,<*a1*>,<*b1*>] where K is Element of Segm 9, a1 is Nat, b1 is Element of Data-Locations : K in {7,8} }
by A3, XBOOLE_0:def 3;
then
ins in { [I,{},<*b,c*>] where I is Element of Segm 9, b, c is Element of Data-Locations : I in {1,2,3,4,5} }
by AMI_3:27, XBOOLE_0:def 3;
then consider I being Element of Segm 9, b, c being Element of Data-Locations such that
A6:
ins = [I,{},<*b,c*>]
and
I in {1,2,3,4,5}
;
reconsider da = b, db = c as Data-Location by Lm1;
take
da
; ex db being Data-Location st ins = AddTo (da,db)
take
db
; ins = AddTo (da,db)
thus
ins = AddTo (da,db)
by A1, A6; verum