sup_inf_self — Mathlib

English

A standard lattice identity holds: (a ∨ b) ∧ (a ∨ c) ∨ (a ∨ b ∧ c) = a ∨ (b ∧ c).

Русский

Стандартное тождество в решётке: (a ∨ b) ∧ (a ∨ c) ∨ (a ∨ (b ∧ c)) = a ∨ (b ∧ c).

LaTeX

$$$((a \lor b) \land (a \lor c)) \lor (a \lor (b \land c)) = a \lor (b \land c)$$$

Lean4

theorem sup_inf_self (a b : α) : a ⊔ a ⊓ b = a :=
  by
  dsimp only [(· ⊔ ·), (· ⊓ ·)]
  rw [← mul_assoc, mul_self, add_assoc, add_self, add_zero]

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