let a, b be Int-Location; :: thesis: for f being FinSeq-Location

for p being preProgram of SCM+FSA st ( b := (f,a) in rng p or (f,a) := b in rng p ) holds

( FirstNotUsed p <> a & FirstNotUsed p <> b )

let f be FinSeq-Location ; :: thesis: for p being preProgram of SCM+FSA st ( b := (f,a) in rng p or (f,a) := b in rng p ) holds

( FirstNotUsed p <> a & FirstNotUsed p <> b )

let p be preProgram of SCM+FSA; :: thesis: ( ( b := (f,a) in rng p or (f,a) := b in rng p ) implies ( FirstNotUsed p <> a & FirstNotUsed p <> b ) )

assume ( b := (f,a) in rng p or (f,a) := b in rng p ) ; :: thesis: ( FirstNotUsed p <> a & FirstNotUsed p <> b )

then consider i being Instruction of SCM+FSA such that

A1: i in rng p and

A2: ( i = b := (f,a) or i = (f,a) := b ) ;

UsedIntLoc i = {a,b} by A2, Th17;

then A3: {a,b} c= UsedILoc p by A1, Th19;

not FirstNotUsed p in UsedILoc p by Th50;

hence ( FirstNotUsed p <> a & FirstNotUsed p <> b ) by A3, ZFMISC_1:32; :: thesis: verum

for p being preProgram of SCM+FSA st ( b := (f,a) in rng p or (f,a) := b in rng p ) holds

( FirstNotUsed p <> a & FirstNotUsed p <> b )

let f be FinSeq-Location ; :: thesis: for p being preProgram of SCM+FSA st ( b := (f,a) in rng p or (f,a) := b in rng p ) holds

( FirstNotUsed p <> a & FirstNotUsed p <> b )

let p be preProgram of SCM+FSA; :: thesis: ( ( b := (f,a) in rng p or (f,a) := b in rng p ) implies ( FirstNotUsed p <> a & FirstNotUsed p <> b ) )

assume ( b := (f,a) in rng p or (f,a) := b in rng p ) ; :: thesis: ( FirstNotUsed p <> a & FirstNotUsed p <> b )

then consider i being Instruction of SCM+FSA such that

A1: i in rng p and

A2: ( i = b := (f,a) or i = (f,a) := b ) ;

UsedIntLoc i = {a,b} by A2, Th17;

then A3: {a,b} c= UsedILoc p by A1, Th19;

not FirstNotUsed p in UsedILoc p by Th50;

hence ( FirstNotUsed p <> a & FirstNotUsed p <> b ) by A3, ZFMISC_1:32; :: thesis: verum