u_inf_l — Mathlib

English

For a preordered β with gi a Galois coinsertion, IsLUB of l''s image yields IsLUB of s under l.

Русский

Для пред-порядка β с Galois Coinsertion, IsLUB(l''s image) приводит к IsLUB s под l.

LaTeX

$$$$ \operatorname{IsLUB}(\{l(s) : s\in S\}, a) \Rightarrow \operatorname{IsLUB}(S, l(a)). $$$$

Lean4

theorem u_inf_l [SemilatticeInf α] [SemilatticeInf β] (gi : GaloisCoinsertion l u) (a b : α) : u (l a ⊓ l b) = a ⊓ b :=
  gi.dual.l_sup_u a b

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