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 Data-Location
for I being Instruction of st I = CurInstr (Computation s1,i) & I = Divide da,db & db in dom p holds
((Computation s1,i) . da) mod ((Computation s1,i) . db) = ((Computation s2,i) . da) mod ((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 Data-Location
for I being Instruction of st I = CurInstr (Computation s1,i) & I = Divide da,db & db in dom p holds
((Computation s1,i) . da) mod ((Computation s1,i) . db) = ((Computation s2,i) . da) mod ((Computation s2,i) . db) )
assume A1: ( p c= s1 & p c= s2 ) ; :: thesis: for i being Element of NAT
for da, db being Data-Location
for I being Instruction of st I = CurInstr (Computation s1,i) & I = Divide da,db & db in dom p holds
((Computation s1,i) . da) mod ((Computation s1,i) . db) = ((Computation s2,i) . da) mod ((Computation s2,i) . db)
let i be Element of NAT ; :: thesis: for da, db being Data-Location
for I being Instruction of st I = CurInstr (Computation s1,i) & I = Divide da,db & db in dom p holds
((Computation s1,i) . da) mod ((Computation s1,i) . db) = ((Computation s2,i) . da) mod ((Computation s2,i) . db)
let da, db be Data-Location ; :: thesis: for I being Instruction of st I = CurInstr (Computation s1,i) & I = Divide da,db & db in dom p holds
((Computation s1,i) . da) mod ((Computation s1,i) . db) = ((Computation s2,i) . da) mod ((Computation s2,i) . db)
let I be Instruction of ; :: thesis: ( I = CurInstr (Computation s1,i) & I = Divide da,db & db in dom p implies ((Computation s1,i) . da) mod ((Computation s1,i) . db) = ((Computation s2,i) . da) mod ((Computation s2,i) . db) )
assume A2: I = CurInstr (Computation s1,i) ; :: thesis: ( not I = Divide da,db or not db in dom p or ((Computation s1,i) . da) mod ((Computation s1,i) . db) = ((Computation s2,i) . da) mod ((Computation s2,i) . db) )
set Cs1i1 = Computation s1,(i + 1);
set Cs1i = Computation s1,i;
set Cs2i1 = Computation s2,(i + 1);
set Cs2i = Computation s2,i;
A3: Computation s2,(i + 1) = Following (Computation s2,i) by AMI_1:14
.= Exec (CurInstr (Computation s2,i)),(Computation s2,i) ;
assume that
A4: I = Divide da,db and
A5: db in dom p and
A6: ((Computation s1,i) . da) mod ((Computation s1,i) . db) <> ((Computation s2,i) . da) mod ((Computation s2,i) . db) ; :: thesis: contradiction
A7: ( ((Computation s1,(i + 1)) | (dom p)) . db = (Computation s1,(i + 1)) . db & ((Computation s2,(i + 1)) | (dom p)) . db = (Computation s2,(i + 1)) . db ) by A5, FUNCT_1:72;
I = CurInstr (Computation s2,i) by A1, A2, Th87;
then A8: (Computation s2,(i + 1)) . db = ((Computation s2,i) . da) mod ((Computation s2,i) . db) by A3, A4, AMI_3:12;
Computation s1,(i + 1) = Following (Computation s1,i) by AMI_1:14
.= Exec (CurInstr (Computation s1,i)),(Computation s1,i) ;
then (Computation s1,(i + 1)) . db = ((Computation s1,i) . da) mod ((Computation s1,i) . db) by A2, A4, AMI_3:12;
hence contradiction by A1, A6, A7, A8, AMI_1:def 25; :: thesis: verum