set S = SCM ;

now

let s be State of ; :: thesis: for o being Object of
for I being Instruction of st InsCode I = InsCode (goto i1) & o <> IC SCM holds
(Exec b₅,b₃) . b₄ = b₃ . b₄
let o be Object of ; :: thesis: for I being Instruction of st InsCode I = InsCode (goto i1) & o <> IC SCM holds
(Exec b₄,b₂) . b₃ = b₂ . b₃
let I be Instruction of ; :: thesis: ( InsCode I = InsCode (goto i1) & o <> IC SCM implies (Exec b₃,b₁) . b₂ = b₁ . b₂ )
assume that
A1: InsCode I = InsCode (goto i1) and
A2: o <> IC SCM ; :: thesis: (Exec b₃,b₁) . b₂ = b₁ . b₂
A3: ex i2 being Instruction-Location of SCM st I = goto i2 by A1, AMI_5:52, MCART_1:7;

per cases ( o in NAT or o is Data-Location ) by A2, Th3;

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

then reconsider l = o as Instruction-Location of SCM by AMI_1:def 4;
l = o ;
hence (Exec I,s) . o = s . o by AMI_1:def 13; :: thesis: verum

end;

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

hence (Exec I,s) . o = s . o by A3, AMI_3:13; :: thesis: verum

end;

end;

end;

hence for b₁ being InsType of st b₁ = InsCode (goto i1) holds
b₁ is jump-only by AMISTD_1:def 3; :: thesis: verum