toOrderHomClass — Mathlib

English

If F is a SupHomClass between semilattice_sup structures, then F is an OrderHomClass.

Русский

Если F является SupHomClass между полузаполненными структурами, то F является OrderHomClass.

LaTeX

$$$$ [\text{SemilatticeSup }\alpha] [\text{SemilatticeSup }\beta] [\text{SupHomClass } F \alpha \beta] \Rightarrow \mathrm{OrderHomClass} F \alpha \beta. $$$$

Lean4

instance (priority := 100) toOrderHomClass [SemilatticeSup α] [SemilatticeSup β] [SupHomClass F α β] :
    OrderHomClass F α β :=
  { ‹SupHomClass F α β› with map_rel := fun f a b h => by rw [← sup_eq_right, ← map_sup, sup_eq_right.2 h] }
    -- See note [lower instance priority]

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