complementedLattice_of_sSup_eq_top

English

A complemented lattice structure arises from the Boolean generators under sSup top.

Русский

Комплектованная решетка появляется из булевых генераторов при верхнем пределе sSup.

LaTeX

$$$ \text{complementedLattice } α $$$

Lean4

theorem complementedLattice_of_sSup_eq_top (hS : BooleanGenerators S) (h : sSup S = ⊤) : ComplementedLattice α :=
  by
  let _i := hS.distribLattice_of_sSup_eq_top h
  have _i₁ := isAtomistic_of_sSup_eq_top hS h
  apply complementedLattice_of_isAtomistic

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