distribLattice — Mathlib

English

A lattice that is a simple order is distributive.

Русский

Ладная система, являющаяся простым порядком, распр.

LaTeX

$$$\mathrm{IsSimpleOrder.distribLattice}(\alpha)$$$

Lean4

/-- A lattice that is a `BoundedOrder` is a distributive lattice.
This is not an instance to prevent loops -/
protected def distribLattice : DistribLattice α :=
  { (inferInstance : Lattice α) with le_sup_inf := fun x y z => by rcases eq_bot_or_eq_top x with (rfl | rfl) <;> simp }
    -- see Note [lower instance priority]

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