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module Core.Environment
import Core.Term
import Core.Term.Thinned
import Core.Thinning
infix 4 =~=
-- Definition ------------------------------------------------------------------
public export
data Env : Nat -> Type where
Lin : Env 0
(:<) : Env n -> Thinned n -> Env (S n)
namespace Eq
public export
data (=~=) : Env n -> Env n -> Type where
Refl : env =~= env
(:<) : env1 =~= env2 -> t =~= u -> env1 :< t =~= env2 :< u
%name Env env
%name Eq.(=~=) prf
-- Indexing --------------------------------------------------------------------
public export
index : Env n -> Fin n -> Thinned n
index (env :< t) FZ = wkn t (wkn1 _)
index (env :< t) (FS i) = wkn (index env i) (wkn1 _)
export
indexCong :
{0 env1, env2 : Env n} ->
env1 =~= env2 ->
(i : Fin n) ->
index env1 i =~= index env2 i
indexCong Refl i = Refl
indexCong (prf :< prf') FZ = wknCong prf' (wkn1 _)
indexCong (prf :< prf') (FS i) = wknCong (indexCong prf i) (wkn1 _)
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