let p be non NAT -defined autonomic FinPartState of ; :: thesis: for s1, s2 being State of SCM+FSA st p c= s1 & p c= s2 holds
for i being Element of NAT
for da being Int-Location
for f being FinSeq-Location st CurInstr (ProgramPart s1),(Comput (ProgramPart s1),s1,i) = da :=len f & da in dom p holds
len ((Comput (ProgramPart s1),s1,i) . f) = len ((Comput (ProgramPart s2),s2,i) . f)
let s1, s2 be State of SCM+FSA ; :: thesis: ( p c= s1 & p c= s2 implies for i being Element of NAT
for da being Int-Location
for f being FinSeq-Location st CurInstr (ProgramPart s1),(Comput (ProgramPart s1),s1,i) = da :=len f & da in dom p holds
len ((Comput (ProgramPart s1),s1,i) . f) = len ((Comput (ProgramPart s2),s2,i) . f) )
assume A1: ( p c= s1 & p c= s2 ) ; :: thesis: for i being Element of NAT
for da being Int-Location
for f being FinSeq-Location st CurInstr (ProgramPart s1),(Comput (ProgramPart s1),s1,i) = da :=len f & da in dom p holds
len ((Comput (ProgramPart s1),s1,i) . f) = len ((Comput (ProgramPart s2),s2,i) . f)
let i be Element of NAT ; :: thesis: for da being Int-Location
for f being FinSeq-Location st CurInstr (ProgramPart s1),(Comput (ProgramPart s1),s1,i) = da :=len f & da in dom p holds
len ((Comput (ProgramPart s1),s1,i) . f) = len ((Comput (ProgramPart s2),s2,i) . f)
let da be Int-Location ; :: thesis: for f being FinSeq-Location st CurInstr (ProgramPart s1),(Comput (ProgramPart s1),s1,i) = da :=len f & da in dom p holds
len ((Comput (ProgramPart s1),s1,i) . f) = len ((Comput (ProgramPart s2),s2,i) . f)
let f be FinSeq-Location ; :: thesis: ( CurInstr (ProgramPart s1),(Comput (ProgramPart s1),s1,i) = da :=len f & da in dom p implies len ((Comput (ProgramPart s1),s1,i) . f) = len ((Comput (ProgramPart s2),s2,i) . f) )
set Cs1i1 = Comput (ProgramPart s1),s1,(i + 1);
set Cs2i1 = Comput (ProgramPart s2),s2,(i + 1);
A2: (Comput (ProgramPart s1),s1,(i + 1)) | (dom p) = (Comput (ProgramPart s2),s2,(i + 1)) | (dom p) by A1, AMI_1:def 25;
set Cs2i = Comput (ProgramPart s2),s2,i;
set Cs1i = Comput (ProgramPart s1),s1,i;
set I = CurInstr (ProgramPart s1),(Comput (ProgramPart s1),s1,i);
A3: Comput (ProgramPart s1),s1,(i + 1) = Following (ProgramPart s1),(Comput (ProgramPart s1),s1,i) by AMI_1:14
.= Exec (CurInstr (ProgramPart s1),(Comput (ProgramPart s1),s1,i)),(Comput (ProgramPart s1),s1,i) ;
A4: ( da in dom p implies ( ((Comput (ProgramPart s1),s1,(i + 1)) | (dom p)) . da = (Comput (ProgramPart s1),s1,(i + 1)) . da & ((Comput (ProgramPart s2),s2,(i + 1)) | (dom p)) . da = (Comput (ProgramPart s2),s2,(i + 1)) . da ) ) by FUNCT_1:72;
A5: Comput (ProgramPart s2),s2,(i + 1) = Following (ProgramPart s2),(Comput (ProgramPart s2),s2,i) by AMI_1:14
.= Exec (CurInstr (ProgramPart s2),(Comput (ProgramPart s2),s2,i)),(Comput (ProgramPart s2),s2,i) ;
assume that
A6: CurInstr (ProgramPart s1),(Comput (ProgramPart s1),s1,i) = da :=len f and
A7: ( da in dom p & len ((Comput (ProgramPart s1),s1,i) . f) <> len ((Comput (ProgramPart s2),s2,i) . f) ) ; :: thesis: contradiction
( (Exec (CurInstr (ProgramPart s1),(Comput (ProgramPart s1),s1,i)),(Comput (ProgramPart s1),s1,i)) . da = len ((Comput (ProgramPart s1),s1,i) . f) & (Exec (CurInstr (ProgramPart s1),(Comput (ProgramPart s1),s1,i)),(Comput (ProgramPart s2),s2,i)) . da = len ((Comput (ProgramPart s2),s2,i) . f) ) by A6, SCMFSA_2:100;
hence contradiction by A1, A3, A5, A4, A2, A7, Th18; :: thesis: verum