let p be non NAT -defined autonomic FinPartState of ; :: thesis: for s1, s2 being State of st p c= s1 & p c= s2 holds
for i being Element of NAT
for da, db being Int-Location st CurInstr (Computation s1,i) = SubFrom da,db & da in dom p holds
((Computation s1,i) . da) - ((Computation s1,i) . db) = ((Computation s2,i) . da) - ((Computation s2,i) . db)
let s1, s2 be State of ; :: thesis: ( p c= s1 & p c= s2 implies for i being Element of NAT
for da, db being Int-Location st CurInstr (Computation s1,i) = SubFrom da,db & da in dom p holds
((Computation s1,i) . da) - ((Computation s1,i) . db) = ((Computation s2,i) . da) - ((Computation s2,i) . db) )
assume A1: ( p c= s1 & p c= s2 ) ; :: thesis: for i being Element of NAT
for da, db being Int-Location st CurInstr (Computation s1,i) = SubFrom da,db & da in dom p holds
((Computation s1,i) . da) - ((Computation s1,i) . db) = ((Computation s2,i) . da) - ((Computation s2,i) . db)
let i be Element of NAT ; :: thesis: for da, db being Int-Location st CurInstr (Computation s1,i) = SubFrom da,db & da in dom p holds
((Computation s1,i) . da) - ((Computation s1,i) . db) = ((Computation s2,i) . da) - ((Computation s2,i) . db)
let da, db be Int-Location ; :: thesis: ( CurInstr (Computation s1,i) = SubFrom da,db & da in dom p implies ((Computation s1,i) . da) - ((Computation s1,i) . db) = ((Computation s2,i) . da) - ((Computation s2,i) . db) )
set I = CurInstr (Computation s1,i);
set Cs1i = Computation s1,i;
set Cs2i = Computation s2,i;
set Cs1i1 = Computation s1,(i + 1);
set Cs2i1 = Computation s2,(i + 1);
A2: Computation s2,(i + 1) = Following (Computation s2,i) by AMI_1:14
.= Exec (CurInstr (Computation s2,i)),(Computation s2,i) ;
A3: ( da in dom p implies ( ((Computation s1,(i + 1)) | (dom p)) . da = (Computation s1,(i + 1)) . da & ((Computation s2,(i + 1)) | (dom p)) . da = (Computation s2,(i + 1)) . da ) ) by FUNCT_1:72;
assume that
A4: CurInstr (Computation s1,i) = SubFrom da,db and
A5: ( da in dom p & ((Computation s1,i) . da) - ((Computation s1,i) . db) <> ((Computation s2,i) . da) - ((Computation s2,i) . db) ) ; :: thesis: contradiction
Computation s1,(i + 1) = Following (Computation s1,i) by AMI_1:14
.= Exec (CurInstr (Computation s1,i)),(Computation s1,i) ;
then A6: (Computation s1,(i + 1)) . da = ((Computation s1,i) . da) - ((Computation s1,i) . db) by A4, SCMFSA_2:91;
CurInstr (Computation s1,i) = CurInstr (Computation s2,i) by A1, Th18;
then (Computation s2,(i + 1)) . da = ((Computation s2,i) . da) - ((Computation s2,i) . db) by A2, A4, SCMFSA_2:91;
hence contradiction by A1, A3, A5, A6, AMI_1:def 25; :: thesis: verum