let p be non NAT -defined autonomic FinPartState of ; :: thesis: for s1, s2 being State of SCM+FSA st NPP p c= s1 & NPP p c= s2 holds
for P1, P2 being the Instructions of SCM+FSA -valued ManySortedSet of NAT st ProgramPart p c= P1 & ProgramPart p c= P2 holds
for i being Element of NAT
for da being Int-Location
for f being FinSeq-Location st CurInstr (P1,(Comput (P1,s1,i))) = da :=len f & da in dom p holds
len ((Comput (P1,s1,i)) . f) = len ((Comput (P2,s2,i)) . f)
let s1, s2 be State of SCM+FSA; :: thesis: ( NPP p c= s1 & NPP p c= s2 implies for P1, P2 being the Instructions of SCM+FSA -valued ManySortedSet of NAT st ProgramPart p c= P1 & ProgramPart p c= P2 holds
for i being Element of NAT
for da being Int-Location
for f being FinSeq-Location st CurInstr (P1,(Comput (P1,s1,i))) = da :=len f & da in dom p holds
len ((Comput (P1,s1,i)) . f) = len ((Comput (P2,s2,i)) . f) )
assume B1: ( NPP p c= s1 & NPP p c= s2 ) ; :: thesis: for P1, P2 being the Instructions of SCM+FSA -valued ManySortedSet of NAT st ProgramPart p c= P1 & ProgramPart p c= P2 holds
for i being Element of NAT
for da being Int-Location
for f being FinSeq-Location st CurInstr (P1,(Comput (P1,s1,i))) = da :=len f & da in dom p holds
len ((Comput (P1,s1,i)) . f) = len ((Comput (P2,s2,i)) . f)
let P1, P2 be the Instructions of SCM+FSA -valued ManySortedSet of NAT ; :: thesis: ( ProgramPart p c= P1 & ProgramPart p c= P2 implies for i being Element of NAT
for da being Int-Location
for f being FinSeq-Location st CurInstr (P1,(Comput (P1,s1,i))) = da :=len f & da in dom p holds
len ((Comput (P1,s1,i)) . f) = len ((Comput (P2,s2,i)) . f) )
assume A2: ( ProgramPart p c= P1 & ProgramPart p c= P2 ) ; :: thesis: for i being Element of NAT
for da being Int-Location
for f being FinSeq-Location st CurInstr (P1,(Comput (P1,s1,i))) = da :=len f & da in dom p holds
len ((Comput (P1,s1,i)) . f) = len ((Comput (P2,s2,i)) . f)
let i be Element of NAT ; :: thesis: for da being Int-Location
for f being FinSeq-Location st CurInstr (P1,(Comput (P1,s1,i))) = da :=len f & da in dom p holds
len ((Comput (P1,s1,i)) . f) = len ((Comput (P2,s2,i)) . f)
let da be Int-Location ; :: thesis: for f being FinSeq-Location st CurInstr (P1,(Comput (P1,s1,i))) = da :=len f & da in dom p holds
len ((Comput (P1,s1,i)) . f) = len ((Comput (P2,s2,i)) . f)
let f be FinSeq-Location ; :: thesis: ( CurInstr (P1,(Comput (P1,s1,i))) = da :=len f & da in dom p implies len ((Comput (P1,s1,i)) . f) = len ((Comput (P2,s2,i)) . f) )
set Cs1i1 = Comput (P1,s1,(i + 1));
set Cs2i1 = Comput (P2,s2,(i + 1));
A3: (Comput (P1,s1,(i + 1))) | (dom (NPP p)) = (Comput (P2,s2,(i + 1))) | (dom (NPP p)) by B1, EXTPRO_1:def 9, A2, B1;
set Cs2i = Comput (P2,s2,i);
set Cs1i = Comput (P1,s1,i);
set I = CurInstr (P1,(Comput (P1,s1,i)));
A4: Comput (P1,s1,(i + 1)) = Following (P1,(Comput (P1,s1,i))) by EXTPRO_1:4
.= Exec ((CurInstr (P1,(Comput (P1,s1,i)))),(Comput (P1,s1,i))) ;
A5: ( da in dom (NPP p) implies ( ((Comput (P1,s1,(i + 1))) | (dom (NPP p))) . da = (Comput (P1,s1,(i + 1))) . da & ((Comput (P2,s2,(i + 1))) | (dom (NPP p))) . da = (Comput (P2,s2,(i + 1))) . da ) ) by FUNCT_1:72;
A6: Comput (P2,s2,(i + 1)) = Following (P2,(Comput (P2,s2,i))) by EXTPRO_1:4
.= Exec ((CurInstr (P2,(Comput (P2,s2,i)))),(Comput (P2,s2,i))) ;
assume that
A7: CurInstr (P1,(Comput (P1,s1,i))) = da :=len f and
A8: ( da in dom p & len ((Comput (P1,s1,i)) . f) <> len ((Comput (P2,s2,i)) . f) ) ; :: thesis: contradiction
A9: da in dom (NPP p) by A8, Lm1;
( (Exec ((CurInstr (P1,(Comput (P1,s1,i)))),(Comput (P1,s1,i)))) . da = len ((Comput (P1,s1,i)) . f) & (Exec ((CurInstr (P1,(Comput (P1,s1,i)))),(Comput (P2,s2,i)))) . da = len ((Comput (P2,s2,i)) . f) ) by A7, SCMFSA_2:100;
hence contradiction by B1, A4, A6, A5, A3, A8, AMISTD_5:7, A9, A2; :: thesis: verum