@MISC{LATWAL_1.MIZ,
  AUTHOR = {Sawicki, Damian and Grabowski, Adam},
  TITLE = {On Weakly Associative Lattices and Near Lattices},
  SECTION1 = {Preliminaries},
  SECTION2 = {Definition of Attributes},
  SECTION3 = {Defining WALs in Terms of the Ordering},
  SECTION4 = {On the Ordering Relation Generated by Weakly Associated Lattices},
  SECTION5 = {Distributivity Gives Associativity},
  SECTION6 = {Near Lattices},
  SECTION7 = {Basic Examples of Near Lattices},
  SECTION8 = {Short Single Axioms for WAL},
  SECTION8 = {WAL-4},
  SECTION9 = {WAL-3 Axioms imply WAL-4},
  SECTION10 = {Distributivities in WAL},
  DAY = {30},
  MONTH = {June},
  YEAR = {2021},
  ADDRESS1 = {Institute of Informatics\\University of Bia{\l}ystok\\Cio{\l}kowskiego 1M, 15-245 Bia{\l}ystok\\Poland},
  ADDRESS2 = {Institute of Informatics\\University of Bia{\l}ystok\\Cio{\l}kowskiego 1M, 15-245 Bia{\l}ystok\\Poland},
  SUMMARY = {The main aim of this article is to introduce formally two 
  generalizations of lattices, namely weakly associative lattices and near lattices,
  which can be obtained from the
  former by certain weakening of the usual well-known laws.
  Some of the results were
  proven in the Mizar system with the help of Prover9 proof assistant, 
  so proofs are definitely lenghty. They can be subject for subsequent revisions
  to make them more compact.}}

