Geodesic
A Simple Solution to the Word Problem for Lattices
Canadian mathematical bulletin, Tome 13 (1970) no. 2, pp. 253-254

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Whitman [2] solved the word problem for lattices by giving an explicit construction of the free lattice, FL(X), on a given set of generators X.The solution is the following:For x, y ∊ X, and a, b, c, d ∊ FL(X), (W1) (W2) (W3) (W4) where [p, q] = {x; p ≤ x ≤ q}.The purpose of this note is to give a simple nonconstructive proof that the condition (W4) must hold in every projective (hence every free) lattice. Jonsson [1] has shown that in every equational class of lattices (Wl), (W2), and (W3) hold. Therefore the combination of these results gives a complete nonconstructive solution to the word problem for lattices. 
Day, Alan. A Simple Solution to the Word Problem for Lattices. Canadian mathematical bulletin, Tome 13 (1970) no. 2, pp. 253-254. doi: 10.4153/CMB-1970-051-0
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     doi = {10.4153/CMB-1970-051-0},
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