bihimp_inf_sup — Mathlib

English

For all a,b, bihimp(a,b) is related to a ∧ b with respect to sup and inf in a precise way: bihimp(a,b) relates to (a ∧ b) via sup/inf identities.

Русский

Для всех a,b биимп(a,b) связан с a ∧ b через тождественные соотношения между sup и inf.

LaTeX

$$$\operatorname{bihimp}(a,b) = \cdot$ (identity with inf and sup terms)$$

Lean4

@[simp]
theorem bihimp_inf_sup : a ⇔ b ⊓ (a ⊔ b) = a ⊓ b :=
  @symmDiff_sup_inf αᵒᵈ _ _ _

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