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This paper tackles the problem of constructing a compact, point-free proof of the associativity of demonic composition of binary relations and its distributivity through demonic choice. In order to achieve this goal a de nition of demonic composition is proposed in which angelic composition is restricted by means of a so-called \monotype factor". Monotype factors are characterised by a Galois connection similar to the Galois connection between composition and factorisation of binary relations.doi:10.1017/s096012950000030x fatcat:fatpcbqnwbbhfal5okcosqsdku