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Difference

Definition: z is a difference of x and y if x = y+z.

x - y := such z: x = z+y.

• Difference is not defined for every x and y:

  There is no z with 1=z+2, thus 1-2 is undefined.

• If a difference exists, it is unique:

  forall x, y, z₀, z₁: (x = z₀+y /\  x = z₁+y) => z₀ = z₁.

• If x >= y, the difference of x and y is defined:

  forall x, y: x >= y => x= (x-y)+y.