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