let a be Int-Location; :: thesis: for f being FinSeq-Location
for p being preProgram of SCM+FSA st ( a :=len f in rng p or f :=<0,...,0> a in rng p ) holds
FirstNotUsed p <> a
let f be FinSeq-Location ; :: thesis: for p being preProgram of SCM+FSA st ( a :=len f in rng p or f :=<0,...,0> a in rng p ) holds
FirstNotUsed p <> a
let p be preProgram of SCM+FSA; :: thesis: ( ( a :=len f in rng p or f :=<0,...,0> a in rng p ) implies FirstNotUsed p <> a )
assume ( a :=len f in rng p or f :=<0,...,0> a in rng p ) ; :: thesis: FirstNotUsed p <> a
then consider i being Instruction of SCM+FSA such that
A1: i in rng p and
A2: ( i = a :=len f or i = f :=<0,...,0> a ) ;
UsedIntLoc i = {a} by A2, Th18;
then A3: {a} c= UsedILoc p by A1, Th19;
not FirstNotUsed p in UsedILoc p by Th50;
hence FirstNotUsed p <> a by A3, ZFMISC_1:31; :: thesis: verum