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Definition

A distributive lattice is a lattice $(L, \leq, \bot, \vee, \top, \wedge)$ with

• a family of dependent terms
  $$a:L, b:L, c: L \vdash a \wedge (b \vee c) = (a \wedge b) \vee (a \wedge c)$$

representing the distributive property for the lattice.

See also

• lattice

• sigma-frame

• Heyting algebra

References

• Alex Simpson, Measure, randomness and sublocales.