lemma for `map` for `⊆` as Subset
mechvel opened this issue · comments
lib-2.0
needs a proof for the following lemma.
map⊆ : (f : C → C') → (f Preserves _≈_ ⟶ _≈'_) → (map f) Preserves _⊆_ ⟶ _⊆'_
This means:
if (f : C → C') , (f Preserves _≈_ ⟶ _≈'_)
,
is a map between the carriers of two setoids that agrees with the two equalities, then it preserves the relation ⊆
of Subset
.
A simlar lemma for Sublist
is provided in Data.List.Relation.Binary.Sublist.Setoid.Properties
.
And the suggested lemma could probably be in
Data.List.Relation.Binary.Subset.Setoid.Properties
.