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...f many sorted functions also have been shown. MML Identifier: MSUALG_3. WWW: http://mizar.org/JFM/Vol6/msualg_3.html The articles [11], [15], [16], [6], [8], [7], [4], [2], [14], [1], [3], [12], [9], =-=[13]-=-, [5], and [10] provide the notation and terminology for this paper. 1. PRELIMINARIES For simplicity, we use the following convention: S is a non void non empty many sorted signature, U1, U2 are algeb...

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...entifier: MSUALG_2. Ewa Burakowska Warsaw University Białystok WWW: http://mizar.org/JFM/Vol6/msualg_2.html The articles [10], [6], [13], [14], [4], [5], [2], [9], [7], [15], [3], [8], [1], [11], and =-=[12]-=- provide the notation and terminology for this paper. 1. AUXILIARY FACTS ABOUT MANY SORTED SETS In this paper x denotes a set. The scheme LambdaB deals with a non empty set A and a unary functor F yie...

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... a many sorted relation are also formulated. MML Identifier: MSUALG_4. WWW: http://mizar.org/JFM/Vol6/msualg_4.html The articles [10], [14], [15], [3], [16], [5], [9], [4], [2], [1], [13], [11], [7], =-=[12]-=-, [6], and [8] provide the notation and terminology for this paper. 1. MANY SORTED RELATION In this paper S denotes a non void non empty many sorted signature, U1 denotes an algebra over S, o denotes ...

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...ne. MML Identifier: PUA2MSS1. WWW: http://mizar.org/JFM/Vol7/pua2mss1.html The articles [14], [19], [18], [7], [1], [12], [20], [21], [4], [15], [3], [8], [6], [5], [22], [13], [10], [11], [2], [16], =-=[17]-=-, and [9] provide the notation and terminology for this paper. 1. Preliminary Let f be a non empty binary relation. One can verify that dom f is non empty and rng f is non empty. Let f be a non-empty ...