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Need fixity#3

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Sofia-Insa wants to merge 11 commits intofixitiesfrom
need-fixity
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Need fixity#3
Sofia-Insa wants to merge 11 commits intofixitiesfrom
need-fixity

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@Sofia-Insa Sofia-Insa commented Aug 18, 2023

Those functions need a fixity.

_≤⊤± :  k  k ≤± ⊤±
⊥±    ≤⊤± = ⊥±≤⊤±
[ k ] ≤⊤± = [ k ]≤⊤±
⊤±    ≤⊤± = ⊤±≤⊤± 

This function establishes that the minimal element ⊥± is less than or equal to all elements k.

_≤⊤± :  k  k ≤± ⊤±
⊥±    ≤⊤± = ⊥±≤⊤±
[ k ] ≤⊤± = [ k ]≤⊤±
⊤±    ≤⊤± = ⊤±≤⊤±

This function establishes that all elements k is less than or equal to the maximal element.
those functions were added agda/agda-stdlib@3cefa71

-- Definition
infix 5 _≤₋_
data _≤₋_ : Rel (A ₋) (a ⊔ ℓ) where
  ⊥₋≤_  : (l : A ₋)          ⊥₋    ≤₋ l
  [_] : {k l : A}  k ≤ l  [ k ] ≤₋ [ l ]

⊥₋≤_ is a constructor

_^⊥ : Container I O c r  Container I O (c ⊔ r) c
(C ^⊥) .Command  o     = (c : C .Command o)  C .Response c
(C ^⊥) .Response {o} _ = C .Command o
(C ^⊥) .next     f c   = C .next c (f c)

agda/agda-stdlib@747351e

data _⊥ (A : Set a) : Set a where
  now   : (x : A)  A ⊥
  later : (x : ∞ (A ⊥))  A ⊥

data _⊥P : Set a  Set (Level.suc a) where
  now   : (x : A)  A ⊥P
  later : (x : ∞ (A ⊥P))  A ⊥P
  _>>=_ : (x : A ⊥P) (f : A  B ⊥P)  B ⊥P

data _⊥ added agda/agda-stdlib@5c22331

agda/agda-stdlib@3aaaab9 data _⊥-whnf added to the file infixl 1 _>>=_
agda/agda-stdlib@c15d12c data _⊥-whnf changed to data _⊥P

Sofia-Insa and others added 11 commits August 4, 2023 12:17
 src/Text/Regex/Derivative/Brzozowski.agda:110,1-114,5 --- _∈?_, _∉?_
 	_∈?_ : Decidable _∈_
 	_∉?_ : Decidable _∉_ 	
 	→  -- binary relations of all kinds are infix 4
 
 src/Text/Regex/Properties.agda:44,1-72,8 --- _∈?[_], _∈?[^\_], _∈?ε, _∈ᴿ?_, _∉ᴿ?_, []∈?_
    → -- binary relations of all kinds are infix 4
-- negation-like  infix  8 ¬_
infix 3  like infix of `_⇔_`
Proposition fixities Relation.Unary.Properties
infix proposition for `_→-cong-⇔_`
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