destructor matemático

teorema constructor:

x < y <==> z+x < z+y

x < y

z+x < z+y

(-z)+z+x < (-z)+z+y

(-0)+x < (-0)+y

x < y

teorema destructor

x < y <==> z+y [< z+x

x < y

¬( z+x < z+y )

z+y [< z+x

teorema constructor:

x [< y <==> z+x [< z+y

x [< y

z+x [< z+y

(-z)+z+x [< (-z)+z+y

(-0)+x [< (-0)+y

x [< y

teorema destructor

x [< y <==> z+y < z+x

x [< y

¬( z+x [< z+y )

z+y < z+x

teorema constructor:

x > y <==> z+x > z+y

x > y

z+x > z+y

(-z)+z+x > (-z)+z+y

(-0)+x > (-0)+y

x > y

teorema destructor

x > y <==> z+y >] z+x

x > y

¬( z+x > z+y )

z+y >] z+x

teorema constructor:

x >] y <==> z+x >] z+y

x >] y

z+x >] z+y

(-z)+z+x >] (-z)+z+y

(-0)+x >] (-0)+y

x >] y

teorema destructor

x >] y <==> z+y > z+x

x >] y

¬( z+x >] z+y )

z+y > z+x

teorema constructor:

x < y <==> x+z < y+z

x < y

x+z < y+z

x+z+(-z) < y+z+(-z)

x+0 < y+0

x < y

teorema destructor

x < y <==> y+z [< x+z

x < y

¬( x+z < y+z )

y+z [< x+z

teorema constructor:

x [< y <==> x+z [< y+z

x [< y

x+z [< y+z

x+z+(-z) [< y+z+(-z)

x+0 [< y+0

x [< y

teorema destructor

x [< y <==> y+z < x+z

x [< y

¬( x+z [< y+z )

y+z < x+z

teorema constructor:

x > y <==> x+z > y+z

x > y

x+z > y+z

x+z+(-z) > y+z+(-z)

x+0 > y+0

x > y

teorema destructor

x > y <==> y+z >] x+z

x > y

¬( x+z > y+z )

y+z >] x+z

teorema constructor:

x >] y <==> x+z >] y+z

x >] y

x+z >] y+z

x+z+(-z) >] y+z+(-z)

x+0 >] y+0

x >] y

teorema destructor

x >] y <==> y+z > x+z

x >] y

¬( x+z >] y+z )

y+z > x+z

teorema constructor:

Si ( ( 0 < x & 0 < y ) || ( x < (-0) & y < (-0) ) ) ==> 0 < x·y

( 0 < x & 0 < y ) || ( x < (-0) & y < (-0) )

( 0 < x & 0 < y ) || ( 0 < (-x) & 0 < (-y) )

( 0·y < x·y & x·0 < x·y ) || ( 0·(-y) < (-x)·(-y) & (-x)·0 < (-x)·(-y) )

( 0 < x·y & 0 < x·y ) || ( 0 < (-x)·(-y) & 0 < (-x)·(-y) )

0 < x·y || 0 < (-x)·(-y)

0 < (1·1)·x·y || 0 < ((-1)·(-1))·x·y

0 < 1·x·y || 0 < 1·x·y

0 < x·y || 0 < x·y

0 < x·y

teorema destructor

Si ( ( 0 < x & 0 < y ) || ( x < (-0) & y < (-0) ) ) ==> x·y [< 0

¬( 0 < x·y )

x·y [< 0