upperClosure_inf_sdiff — Mathlib

English

The dual statement to sdiff_inf_upperClosure: upperClosure(t) ∧ (s.sdiff t) = s.

Русский

Двойственное утверждение к upperClosure_inf_sdiff: верхнее пересечение (s.sdiff t) с upperClosure(t) даёт s.

LaTeX

$$$\\operatorname{upperClosure}(t) \\sqcap (s.sdiff t) = s$$$

Lean4

theorem upperClosure_inf_sdiff (hts : t ⊆ s) (hst : ∀ b ∈ s, ∀ c ∈ t, b ≤ c → b ∈ t) : upperClosure t ⊓ s.sdiff t = s :=
  by rw [inf_comm, sdiff_inf_upperClosure hts hst]

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