#!perl -T -w

use strict;
#use wtf8;

my ($kappa,$mu) = (0,2);
print "Is $kappa lesser than $mu ?:\n"; 
printf "%8s%s%-4s%s\n",'$kappa',' < ','$mu','-> boolean context';

my $bool = $kappa < $mu;
printf "%8d%s%-4d%s%d\n","$kappa",' < ',"$mu",'-> ', $bool;

while( ++$kappa  ){ # prefix increment
 $bool = $kappa < $mu;
 printf "%8d%s%-4d%s%d\n",$kappa,' < ',$mu, '-> ',$bool;
 last if $kappa == 3;
}
__END__
#OUTPUT
  $kappa < $mu -> boolean context
       0 < 2   -> 1
       1 < 2   -> 1
       2 < 2   -> 0
       3 < 2   -> 0

##</code><code>##

($kappa,$mu) = (0,2);
print "Is $kappa lesser than $mu ?:\n"; 
printf "%8s%s%-4s%s\n",'$kappa',' < ','$mu','-> boolean context';

$bool = $kappa < $mu;
printf "%8d%s%-4d%s%2d\n",$kappa,' < ',$mu, '-> ',$bool;

while( $kappa++  ){ # postfix increment
 $bool = $kappa < $mu;
 printf "%8d%s%-4d%s%2d\n",$kappa,' < ',$mu, '-> ',$bool;
 last if $kappa == 3;
}
printf "Where is my table?\n";
__END__
#OUTPUT
Is 0 lesser than 2 ?:
  $kappa < $mu -> boolean context
       0 < 2   ->  1
Where is my table?

##</code><code>##

($kappa,$mu) = (0,2);

printf "%s\n",'$kappa < $mu -> boolean -> value we ask perl to return';

$bool = $kappa < $mu;
my $ret_value;

if( $kappa < $mu ){   # if( $bool )
   $ret_value = sprintf "%-8s%d", '$kappa: ',$kappa;
}else{
   $ret_value = sprintf "%-8s%d", '$mu: ',$mu;
}

printf "%8d%s%-4d%s%-11d%s%s\n",$kappa,' < ',$mu,' -> ',$bool,'-> ',$ret_value;

while( ++$kappa  ){
 $bool = $kappa < $mu;
 if( $kappa < $mu ){   # if( $bool )
   $ret_value = sprintf "%-8s%d", '$kappa: ',$kappa;
 }else{
   $ret_value = sprintf "%-8s%d", '$mu: ',$mu;
 }

 printf "%8d%s%-4d%s%-11d%s%s\n",$kappa,' < ',$mu,' -> ',$bool,'-> ',$ret_value;

 last if $kappa == 3;
}
__END__
$kappa < $mu -> boolean -> value we ask perl to return
       0 < 2    -> 1          -> $kappa: 0
       1 < 2    -> 1          -> $kappa: 1
       2 < 2    -> 0          -> $mu:    2
       3 < 2    -> 0          -> $mu:    2

##</code><code>##

while( $kappa < $mu  ){

$ret_value = $kappa

}

##</code><code>##

print qq{\n};

($kappa,$mu) = (0,15);

$bool = $kappa < $mu;

if( $kappa < $mu ){   # if( $bool )
   $ret_value = sprintf "%-8s%d", '$kappa: ',$kappa;
}else{
   $ret_value = sprintf "%-8s%d", '$mu: ',$mu;
}

printf "%8d%s%-4d%s%-11d%s%s\n",$kappa,' < ',$mu,' -> ',$bool,'-> ',$ret_value;
__END__
$kappa < $mu -> boolean -> value we ask perl to return
       0 < 15   -> 1          -> $kappa: 0

##</code><code>##

print qq{\n};

$kappa++ until( $kappa > $mu );

$bool = $kappa < $mu;

if( $kappa < $mu ){   # if( $bool )
   $ret_value = sprintf "%-8s%d", '$kappa: ',$kappa;
}else{
   $ret_value = sprintf "%-8s%d", '$mu: ',$mu;
}

printf "%8d%s%-4d%s%-11d%s%s\n",$kappa,' < ',$mu,' -> ',$bool,'-> ',$ret_value;
__END__
$kappa < $mu -> boolean -> value we ask perl to return
      16 < 15   -> 0          -> $mu:    15

##</code><code>##


# An approach to coding the proof for Distribution rule
# for Summation and Union over the Natural Realm
# re MF:C:155


my($nu,$lhs,$rhs);
($kappa,$mu,$nu) = (3,4,5);
if( $kappa < $mu and $mu < $nu ){
  print "Evaluating relation when \$kappa:$kappa < \$mu:$mu < \$nu:$nu\n";
  $lhs =  $kappa + ( $mu < $nu ? $nu : $mu ); 
  $rhs =  ( $kappa + $mu ) < ( $kappa + $nu ) ?  $kappa + $nu : $kappa + $mu ;
  print "\$lhs:$lhs  = \$kappa:$kappa + \$nu:$nu\n";
  print "\$rhs:$rhs  = \$kappa:$kappa + \$nu:$nu\n";
  print "Evaluation of relation ", $lhs == $rhs ? 'succeeded' : 'failed';
  print qq{\n};
 
}

until( $kappa > $mu and $mu > $nu  ){
 $mu *= $mu unless $mu > $nu;
 $kappa *= $kappa unless $kappa > $mu;
# print "\$kappa:$kappa \$mu:$mu \$nu:$nu\n";

}

#print "\$kappa:$kappa > \$mu:$mu > \$nu:$mu"

#now we have interchanged the values not the operators 

if( $nu < $mu and $mu < $kappa ){
  print "Evaluating relation when \$nu:$nu < \$mu:$mu < \$kappa:$kappa\n";
  $lhs =  $nu + ( $mu > $kappa ?  $mu : $kappa ); 
#  $rhs =  ( $nu > $mu ? $nu : $mu ) + ( $nu < $kappa ? $nu : $kappa );
  $rhs =  ( $nu + $mu ) > ( $nu + $kappa ) ?  $nu + $mu : $nu + $kappa ;
  print "\$lhs:$lhs  = \$kappa:$kappa + \$mu:$mu\n";
  print "\$rhs:$rhs  = \$kappa:$kappa + \$mu:$mu\n";
  print "Evaluation of relation ", $lhs == $rhs ? 'succeeded' : 'failed'; 
  print qq{\n};

}
__END__
Evaluating relation when $kappa:3 < $mu:4 < $nu:5
$lhs:8  = $kappa:3 + $nu:5
$rhs:8  = $kappa:3 + $nu:5
Evaluation of relation succeeded
Evaluating relation when $nu:5 < $mu:16 < $kappa:81
$lhs:86  = $kappa:81 + $mu:16
$rhs:86  = $kappa:81 + $mu:16
Evaluation of relation succeeded

##</code><code>##

print qq{\nAn approach to the proof of the Distribution Rule for\n};
print qq{Summation and Union over the Natural Realm wrt MF(C):155 P.NJW\n};

# An approach to coding the proof for Distribution rule
# for Summation and Union over the Natural Realm
# re MF:C:155

#my($nu,$lhs,$rhs);
($kappa,$mu,$nu) = (3,4,5);


until( $kappa < $mu and $mu < $nu  ){ # skips this, already satisfied
 $mu *= $mu unless $mu > $nu;
 $kappa *= $kappa unless $kappa > $mu;
 print "\$kappa:$kappa \$mu:$mu \$nu:$nu\n";
}

print "\nEvaluating relation (P1) when \$kappa:$kappa < \$mu:$mu < \$nu:$nu\n";

$lhs =  $kappa + ( $mu < $nu ? $nu : $mu ); 
$rhs =  ( $kappa + $mu ) < ( $kappa + $nu ) ?  $kappa + $nu : $kappa + $mu ;
print "\$lhs:$lhs  = \$kappa:$kappa + \$nu:$nu\n";
print "\$rhs:$rhs  = \$kappa:$kappa + \$nu:$nu\n";
print "Evaluation of relation ", $lhs == $rhs ? 'succeeded' : 'failed';
print qq{\n};



until( $kappa < $nu and $nu < $mu  ){
 $mu *= $mu unless $mu > $nu;
 $nu *= $nu unless $nu > $kappa;
# print "\$kappa:$kappa \$nu:$nu \$mu:$mu\n";
}

print "\nEvaluating relation when (P2) \$kappa:$kappa < \$nu:$nu < \$mu:$mu\n";

$lhs =  $kappa + ( $mu < $nu ? $nu : $mu ); 
$rhs =  ( $kappa + $mu ) < ( $kappa + $nu ) ?  $kappa + $nu : $kappa + $mu ;
print "\$lhs:$lhs  = \$kappa:$kappa + \$mu:$mu\n";
print "\$rhs:$rhs  = \$kappa:$kappa + \$mu:$mu\n";
print "Evaluation of relation ", $lhs == $rhs ? 'succeeded' : 'failed';
print qq{\n};



until( $mu < $kappa and $kappa < $nu  ){
 $nu *= $nu unless $nu > $kappa;
 $kappa *= $kappa unless $kappa > $mu;
# print "\$mu:$mu \$kappa:$kappa \$nu:$nu\n";
}

print "\nEvaluating relation (P3) when \$mu:$mu < \$kappa:$kappa < \$nu:$nu\n";

$lhs =  $mu + ( $kappa < $nu ? $nu : $kappa ); 
$rhs =  ( $mu + $kappa ) < ( $mu + $nu ) ?  $mu + $nu : $mu + $kappa ;
print "\$lhs:$lhs  = \$mu:$mu + \$nu:$nu\n";
print "\$rhs:$rhs  = \$mu:$mu + \$nu:$nu\n";
print "Evaluation of relation ", $lhs == $rhs ? 'succeeded' : 'failed';
print qq{\n};



until( $mu < $nu and $nu < $kappa  ){
 $kappa *= $kappa unless $kappa > $nu;
 $nu *= $nu unless $nu > $mu;
# print "\$mu:$mu \$nu:$nu \$kappa:$kappa\n";
}

print "\nEvaluating relation (P4) when \$mu:$mu < \$nu:$nu < \$kappa:$kappa\n";

$lhs =  $mu + ( $kappa < $nu ? $nu : $kappa ); 
$rhs =  ( $mu + $kappa ) < ( $mu + $nu ) ?  $mu + $nu : $mu + $kappa ;
print "\$lhs:$lhs  = \$mu:$mu + \$nu:$nu\n";
print "\$rhs:$rhs  = \$mu:$mu + \$nu:$nu\n";
print "Evaluation of relation ", $lhs == $rhs ? 'succeeded' : 'failed';
print qq{\n};



until( $nu < $kappa and $kappa < $mu  ){
 $mu *= $mu unless $mu > $kappa;
 $kappa *= $kappa unless $kappa > $nu;
# print "\$nu:$nu \$kappa:$kappa \$mu:$mu\n";
}

print "\nEvaluating relation (P5) when \$nu:$nu < \$kappa:$kappa < \$mu:$mu\n";

$lhs =  $nu + ( $mu > $kappa ?  $mu : $kappa ); 
$rhs =  ( $nu + $mu ) > ( $nu + $kappa ) ?  $nu + $mu : $nu + $kappa ;
print "\$lhs:$lhs  = \$kappa:$kappa + \$mu:$mu\n";
print "\$rhs:$rhs  = \$kappa:$kappa + \$mu:$mu\n";
print "Evaluation of relation ", $lhs == $rhs ? 'succeeded' : 'failed'; 
print qq{\n};




until( $nu < $mu and $mu < $kappa  ){
 $kappa *= $kappa unless $kappa > $mu;
 $mu *= $mu unless $mu > $nu;
# print "\$nu:$nu \$mu:$mu \$kappa:$kappa\n";
}

print "\nEvaluating relation (P6) when \$nu:$nu < \$mu:$mu < \$kappa:$kappa\n";

$lhs =  $nu + ( $mu > $kappa ?  $mu : $kappa ); 
$rhs =  ( $nu + $mu ) > ( $nu + $kappa ) ?  $nu + $mu : $nu + $kappa ;
print "\$lhs:$lhs  = \$kappa:$kappa + \$mu:$mu\n";
print "\$rhs:$rhs  = \$kappa:$kappa + \$mu:$mu\n";
print "Evaluation of relation ", $lhs == $rhs ? 'succeeded' : 'failed'; 
print qq{\n\n};

##</code><code>##

An approach to the proof of the Distribution Rule for
Summation and Union over the Natural Realm wrt MF(C):155 P.NJW

Evaluating relation (P1) when $kappa:3 < $mu:4 < $nu:5
$lhs:8  = $kappa:3 + $nu:5
$rhs:8  = $kappa:3 + $nu:5
Evaluation of relation succeeded

Evaluating relation when (P2) $kappa:3 < $nu:5 < $mu:16
$lhs:19  = $kappa:3 + $mu:16
$rhs:19  = $kappa:3 + $mu:16
Evaluation of relation succeeded

Evaluating relation (P3) when $mu:16 < $kappa:81 < $nu:625
$lhs:641  = $mu:16 + $nu:625
$rhs:641  = $mu:16 + $nu:625
Evaluation of relation succeeded

Evaluating relation (P4) when $mu:16 < $nu:625 < $kappa:6561
$lhs:6577  = $mu:16 + $nu:625
$rhs:6577  = $mu:16 + $nu:625
Evaluation of relation succeeded

Evaluating relation (P5) when $nu:625 < $kappa:6561 < $mu:65536
$lhs:66161  = $kappa:6561 + $mu:65536
$rhs:66161  = $kappa:6561 + $mu:65536
Evaluation of relation succeeded

Evaluating relation (P6) when $nu:625 < $mu:65536 < $kappa:43046721
$lhs:43047346  = $kappa:43046721 + $mu:65536
$rhs:43047346  = $kappa:43046721 + $mu:65536
Evaluation of relation succeeded