set S = SCM+FSA ;

now

let s be State of SCM+FSA ; :: thesis: for o being Object of SCM+FSA
for I being Instruction of SCM+FSA st InsCode I = InsCode (a >0_goto i1) & o <> IC SCM+FSA holds
(Exec b₅,b₃) . b₄ = b₃ . b₄
let o be Object of SCM+FSA ; :: thesis: for I being Instruction of SCM+FSA st InsCode I = InsCode (a >0_goto i1) & o <> IC SCM+FSA holds
(Exec b₄,b₂) . b₃ = b₂ . b₃
let I be Instruction of SCM+FSA ; :: thesis: ( InsCode I = InsCode (a >0_goto i1) & o <> IC SCM+FSA implies (Exec b₃,b₁) . b₂ = b₁ . b₂ )
assume that
A4: InsCode I = InsCode (a >0_goto i1) and
A5: o <> IC SCM+FSA ; :: thesis: (Exec b₃,b₁) . b₂ = b₁ . b₂
A6: ex i2 being Element of NAT ex b being Int-Location st I = b >0_goto i2 by A4, SCMFSA_2:49, SCMFSA_2:61;

per cases ( o in NAT or o is Int-Location or o is FinSeq-Location ) by A5, Th7;

suppose o in NAT ; :: thesis: (Exec b₃,b₁) . b₂ = b₁ . b₂

then reconsider l = o as Element of NAT ;
l = o ;
hence (Exec I,s) . o = s . o by AMI_1:def 13; :: thesis: verum

end;

suppose o is Int-Location ; :: thesis: (Exec b₃,b₁) . b₂ = b₁ . b₂

hence (Exec I,s) . o = s . o by A6, SCMFSA_2:97; :: thesis: verum

end;

suppose o is FinSeq-Location ; :: thesis: (Exec b₃,b₁) . b₂ = b₁ . b₂

hence (Exec I,s) . o = s . o by A6, SCMFSA_2:97; :: thesis: verum

end;

end;

end;

hence for b₁ being InsType of SCM+FSA st b₁ = InsCode (a >0_goto i1) holds
b₁ is jump-only by AMISTD_1:def 3; :: thesis: verum