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

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