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*Proposition:* Every quasi order is antisymmetric:

forallS,<:<is quasi order onS=><is antisymmetric onS.

*Proof:*
Take arbitrary `S` and quasi order **<** on `S`. Assume there
exist `x` in `S` and `y` in `S` with
`x` != `y` such that `x` **<** `y` and `y`
**<** `x`. By transitivity, we have `x` **<** `x`
which contradicts the irreflexivity of **<** .

*Only difference between partial orders and quasi orders is
reflexivity versus irreflexivity.*

Author: Wolfgang Schreiner

Last Modification: January 18, 2000