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Definition
A binary relation over a type is a strict order (also called strict total order, strict linear order, or pseudo-order ) if on it a comes type with is a type family on with
a family of dependent terms
representing that the irreflexivity dependent condition type for is the a binary proposition relation
a family of dependent terms
representing the comparison irreflexivity condition for the binary dependent relation type
a family of dependent terms
representing the connectedness comparison condition for the binary dependent relation type
a family of dependent terms
representing the asymmetry connectedness condition for the binary dependent relation type
a family of dependent terms
representing the asymmetry condition for the dependent type