English
A generalized implication operation HImp is defined on nuclei, generalizing Heyting algebra implication.
Русский
Определён обобщённый операция импликации HImp на нуклеусах, обобщая импликацию в Heyting-алгебре.
LaTeX
$$$\text{HImp}(m,n)$ is a nucleus-valued implication$$
Lean4
theorem map_himp_le : n (x ⇨ y) ≤ x ⇨ n y := by
rw [le_himp_iff]
calc
n (x ⇨ y) ⊓ x
_ ≤ n (x ⇨ y) ⊓ n x := by gcongr; exact n.le_apply
_ = n (y ⊓ x) := by rw [← map_inf, himp_inf_self]
_ ≤ n y := by gcongr; exact inf_le_left