exists_inf_eq_and_codisjoint — Mathlib

English

Equivalence: IsModularLattice α iff ∀ x,y,z, (x ∧ z) ∨ (y ∧ z) = (x ∨ y) ∧ z.

Русский

Эквивалентность: IsModularLattice α эквивалентно ∀ x,y,z, (x ∧ z) ∨ (y ∧ z) = (x ∨ y) ∧ z.

LaTeX

$$$\text{IsModularLattice }\alpha \iff \forall x,y,z:\; (x\wedge z)\vee(y\wedge z)=(x\vee y)\wedge z.$$$

Lean4

theorem exists_inf_eq_and_codisjoint (h : a ≤ b) : ∃ b', b ⊓ b' = a ∧ Codisjoint b b' :=
  by
  simp_rw [codisjoint_iff]
  apply exists_inf_eq_and_sup_eq h (by simp)

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