Add certain proofs for ``_∤_``
mechvel opened this issue · comments
I suggest to add to Algebra.Definitions.RawMagma
the proofs for _∤_
which are similar to the proofs
∣-respʳ, ∣-respˡ, ∣-resp
.
For example, like this:
∤-respˡ : {x : C} → (_∤ x) Respects _≈_
∤-respˡ y≈y' y∤x y'∣x = y∤x y∣x where
y∣x = ∣-respˡ (sym y≈y') y'∣x
∤-respʳ : {x : C} → (x ∤_) Respects _≈_
∤-respʳ = ...
∤-resp : _∤_ Respects₂ _≈_
∤-resp = ...
Otherwise almost everyone who programs algebra would have to implement them oneself.
They can't live in Algebra.Definitions.RawMagma
as you don't have a proof that the relation is an equality.
Instead these already exist in Algebra.Properties.Magma.Divisibility
:
https://github.com/agda/agda-stdlib/blob/master/src/Algebra/Properties/Magma/Divisibility.agda
I do not see these lemmas in Algebra.Properties.Magma.Divisibility in lib-2.0.
Do you mean that they have to appear in the next official version?
No, they exist in v2.0 as well:
https://github.com/agda/agda-stdlib/blob/v2.0/src/Algebra/Properties/Magma/Divisibility.agda
I see there that _∤_
is imported,
but I do not see there the three suggested proofs
∤-resp : _∤_ Respects₂ _≈_
...
For any occasion: the last nonempty line in this file is of number 54.
Lines 26-33
These lines concern _∣_
- divisibility.
And I talk about _∤_
- negation of divisibility.
Are you saying that ∣-respʳ
is also a proof for _∤_ Respectsʳ _≈_
?
(I think, it is not).
Or may be your GitHub editor does not show the symbol ∤
("does not divide") correctly?
Ah sorry, yes my mistake, these are indeed missing and should be added just below.