let a be Int-Location ; :: thesis: for l being Instruction-Location of SCM+FSA
for p being preProgram of SCM+FSA st ( a =0_goto l in rng p or a >0_goto l in rng p ) holds
FirstNotUsed p <> a
let l be Instruction-Location of SCM+FSA ; :: thesis: for p being preProgram of SCM+FSA st ( a =0_goto l in rng p or a >0_goto l in rng p ) holds
FirstNotUsed p <> a
let p be preProgram of SCM+FSA ; :: thesis: ( ( a =0_goto l in rng p or a >0_goto l in rng p ) implies FirstNotUsed p <> a )
assume ( a =0_goto l in rng p or a >0_goto l in rng p ) ; :: thesis: FirstNotUsed p <> a
then consider i being Instruction of SCM+FSA such that
A1: ( i in rng p & ( i = a =0_goto l or i = a >0_goto l ) ) ;
UsedIntLoc i = {a} by A1, Th20;
then ( {a} c= UsedIntLoc p & not FirstNotUsed p in UsedIntLoc p ) by A1, Th23, Th54;
hence FirstNotUsed p <> a by ZFMISC_1:37; :: thesis: verum