let I be Program of SCM+FSA ; :: thesis: for a being Int-Location
for l being Instruction-Location of SCM+FSA holds not a in dom (I +* (Start-At l))
let a be Int-Location ; :: thesis: for l being Instruction-Location of SCM+FSA holds not a in dom (I +* (Start-At l))
let l be Instruction-Location of SCM+FSA ; :: thesis: not a in dom (I +* (Start-At l))
assume a in dom (I +* (Start-At l)) ; :: thesis: contradiction
then a in (dom I) \/ (dom (Start-At l)) by FUNCT_4:def 1;
then A1: ( a in dom I or a in dom (Start-At l) ) by XBOOLE_0:def 3;
A2: dom I c= NAT by RELAT_1:def 18;
a in Int-Locations by SCMFSA_2:9;
hence contradiction by A1, A2, Th9, SCMFSA_2:13, XBOOLE_0:3; :: thesis: verum