hereby :: thesis: ( ( ( InsCode i = 7 or InsCode i = 8 ) implies ex b₁ being Element of Fin Int-Locations ex a being Int-Location ex l being Nat st
( ( i = a =0_goto l or i = a >0_goto l ) & b₁ = {a} ) ) & ( ( InsCode i = 9 or InsCode i = 10 ) implies ex b₁ being Element of Fin Int-Locations ex a, b being Int-Location ex f being FinSeq-Location st
( ( i = b := (f,a) or i = (f,a) := b ) & b₁ = {a,b} ) ) & ( ( InsCode i = 11 or InsCode i = 12 ) implies ex b₁ being Element of Fin Int-Locations ex a being Int-Location ex f being FinSeq-Location st
( ( i = a :=len f or i = f :=<0,...,0> a ) & b₁ = {a} ) ) & ( InsCode i in {1,2,3,4,5} or InsCode i = 7 or InsCode i = 8 or InsCode i = 9 or InsCode i = 10 or InsCode i = 11 or InsCode i = 12 or ex b₁ being Element of Fin Int-Locations st b₁ = {} ) )

assume InsCode i in {1,2,3,4,5} ; :: thesis: ex IT being Element of Fin Int-Locations ex a, b being Int-Location st
( ( i = a := b or i = AddTo (a,b) or i = SubFrom (a,b) or i = MultBy (a,b) or i = Divide (a,b) ) & IT = {a,b} )
then not not InsCode i = 1 & ... & not InsCode i = 5 by ENUMSET1:def 3;
then consider a, b being Int-Location such that
A1: ( i = a := b or i = AddTo (a,b) or i = SubFrom (a,b) or i = MultBy (a,b) or i = Divide (a,b) ) by SCMFSA_2:30, SCMFSA_2:31, SCMFSA_2:32, SCMFSA_2:33, SCMFSA_2:34;
reconsider a9 = a, b9 = b as Element of Int-Locations by AMI_2:def 16;
reconsider IT = {.a9,b9.} as Element of Fin Int-Locations ;
take IT = IT; :: thesis: ex a, b being Int-Location st
( ( i = a := b or i = AddTo (a,b) or i = SubFrom (a,b) or i = MultBy (a,b) or i = Divide (a,b) ) & IT = {a,b} )
take a = a; :: thesis: ex b being Int-Location st
( ( i = a := b or i = AddTo (a,b) or i = SubFrom (a,b) or i = MultBy (a,b) or i = Divide (a,b) ) & IT = {a,b} )
take b = b; :: thesis: ( ( i = a := b or i = AddTo (a,b) or i = SubFrom (a,b) or i = MultBy (a,b) or i = Divide (a,b) ) & IT = {a,b} )
thus ( ( i = a := b or i = AddTo (a,b) or i = SubFrom (a,b) or i = MultBy (a,b) or i = Divide (a,b) ) & IT = {a,b} ) by A1; :: thesis: verum

end;

hereby :: thesis: ( ( ( InsCode i = 9 or InsCode i = 10 ) implies ex b₁ being Element of Fin Int-Locations ex a, b being Int-Location ex f being FinSeq-Location st
( ( i = b := (f,a) or i = (f,a) := b ) & b₁ = {a,b} ) ) & ( ( InsCode i = 11 or InsCode i = 12 ) implies ex b₁ being Element of Fin Int-Locations ex a being Int-Location ex f being FinSeq-Location st
( ( i = a :=len f or i = f :=<0,...,0> a ) & b₁ = {a} ) ) & ( InsCode i in {1,2,3,4,5} or InsCode i = 7 or InsCode i = 8 or InsCode i = 9 or InsCode i = 10 or InsCode i = 11 or InsCode i = 12 or ex b₁ being Element of Fin Int-Locations st b₁ = {} ) )

assume ( InsCode i = 7 or InsCode i = 8 ) ; :: thesis: ex IT being Element of Fin Int-Locations ex a being Int-Location ex l being Nat st
( ( i = a =0_goto l or i = a >0_goto l ) & IT = {a} )
then consider l being Nat, a being Int-Location such that
A2: ( i = a =0_goto l or i = a >0_goto l ) by SCMFSA_2:36, SCMFSA_2:37;
reconsider a9 = a as Element of Int-Locations by AMI_2:def 16;
reconsider IT = {.a9.} as Element of Fin Int-Locations ;
take IT = IT; :: thesis: ex a being Int-Location ex l being Nat st
( ( i = a =0_goto l or i = a >0_goto l ) & IT = {a} )
take a = a; :: thesis: ex l being Nat st
( ( i = a =0_goto l or i = a >0_goto l ) & IT = {a} )
take l = l; :: thesis: ( ( i = a =0_goto l or i = a >0_goto l ) & IT = {a} )
thus ( ( i = a =0_goto l or i = a >0_goto l ) & IT = {a} ) by A2; :: thesis: verum

end;

hereby :: thesis: ( ( ( InsCode i = 11 or InsCode i = 12 ) implies ex b₁ being Element of Fin Int-Locations ex a being Int-Location ex f being FinSeq-Location st
( ( i = a :=len f or i = f :=<0,...,0> a ) & b₁ = {a} ) ) & ( InsCode i in {1,2,3,4,5} or InsCode i = 7 or InsCode i = 8 or InsCode i = 9 or InsCode i = 10 or InsCode i = 11 or InsCode i = 12 or ex b₁ being Element of Fin Int-Locations st b₁ = {} ) )

assume ( InsCode i = 9 or InsCode i = 10 ) ; :: thesis: ex IT being Element of Fin Int-Locations ex a, b being Int-Location ex f being FinSeq-Location st
( ( i = b := (f,a) or i = (f,a) := b ) & IT = {a,b} )
then consider a, b being Int-Location, f being FinSeq-Location such that
A3: ( i = b := (f,a) or i = (f,a) := b ) by SCMFSA_2:38, SCMFSA_2:39;
reconsider a9 = a, b9 = b as Element of Int-Locations by AMI_2:def 16;
reconsider IT = {.a9,b9.} as Element of Fin Int-Locations ;
take IT = IT; :: thesis: ex a, b being Int-Location ex f being FinSeq-Location st
( ( i = b := (f,a) or i = (f,a) := b ) & IT = {a,b} )
take a = a; :: thesis: ex b being Int-Location ex f being FinSeq-Location st
( ( i = b := (f,a) or i = (f,a) := b ) & IT = {a,b} )
take b = b; :: thesis: ex f being FinSeq-Location st
( ( i = b := (f,a) or i = (f,a) := b ) & IT = {a,b} )
take f = f; :: thesis: ( ( i = b := (f,a) or i = (f,a) := b ) & IT = {a,b} )
thus ( ( i = b := (f,a) or i = (f,a) := b ) & IT = {a,b} ) by A3; :: thesis: verum

end;

hereby :: thesis: ( InsCode i in {1,2,3,4,5} or InsCode i = 7 or InsCode i = 8 or InsCode i = 9 or InsCode i = 10 or InsCode i = 11 or InsCode i = 12 or ex b₁ being Element of Fin Int-Locations st b₁ = {} )

assume ( InsCode i = 11 or InsCode i = 12 ) ; :: thesis: ex IT being Element of Fin Int-Locations ex a being Int-Location ex f being FinSeq-Location st
( ( i = a :=len f or i = f :=<0,...,0> a ) & IT = {a} )
then consider a being Int-Location, f being FinSeq-Location such that
A4: ( i = a :=len f or i = f :=<0,...,0> a ) by SCMFSA_2:40, SCMFSA_2:41;
reconsider a9 = a as Element of Int-Locations by AMI_2:def 16;
reconsider IT = {.a9.} as Element of Fin Int-Locations ;
take IT = IT; :: thesis: ex a being Int-Location ex f being FinSeq-Location st
( ( i = a :=len f or i = f :=<0,...,0> a ) & IT = {a} )
take a = a; :: thesis: ex f being FinSeq-Location st
( ( i = a :=len f or i = f :=<0,...,0> a ) & IT = {a} )
take f = f; :: thesis: ( ( i = a :=len f or i = f :=<0,...,0> a ) & IT = {a} )
thus ( ( i = a :=len f or i = f :=<0,...,0> a ) & IT = {a} ) by A4; :: thesis: verum

end;

{} in Fin Int-Locations by FINSUB_1:7;
hence ( InsCode i in {1,2,3,4,5} or InsCode i = 7 or InsCode i = 8 or InsCode i = 9 or InsCode i = 10 or InsCode i = 11 or InsCode i = 12 or ex b₁ being Element of Fin Int-Locations st b₁ = {} ) ; :: thesis: verum