@@ -41,7 +41,7 @@ Section Definitions.
4141 | typeNeuConvAlg {Γ M N T} :
4242 whne M ->
4343 whne N ->
44- [ Γ |- M ~ N ▹ T] ->
44+ [ Γ |- M ~ N ▹ T] ->
4545 [ Γ |- M ≅h N]
4646 (** **** Conversion of neutral terms *)
4747 with ConvNeuAlg : context -> term -> term -> term -> Type :=
@@ -110,7 +110,7 @@ Section Definitions.
110110 | termFunConvAlg {Γ : context} {f g A B} :
111111 whnf f ->
112112 whnf g ->
113- [ Γ,, A |- eta_expand f ≅ eta_expand g : B] ->
113+ [ Γ,, A |- eta_expand f ≅ eta_expand g : B] ->
114114 [ Γ |- f ≅h g : tProd A B]
115115 | termSigCongAlg {Γ A B A' B'} :
116116 [ Γ |- A ≅ A' : U] ->
@@ -119,8 +119,8 @@ Section Definitions.
119119 | termPairConvAlg {Γ : context} {p q A B} :
120120 whnf p ->
121121 whnf q ->
122- [ Γ |- tFst p ≅ tFst q : A] ->
123- [ Γ |- tSnd p ≅ tSnd q : B[(tFst p)..]] ->
122+ [ Γ |- tFst p ≅ tFst q : A] ->
123+ [ Γ |- tSnd p ≅ tSnd q : B[(tFst p)..]] ->
124124 [ Γ |- p ≅h q : tSig A B]
125125 | termIdCongAlg {Γ A A' x x' y y'} :
126126 [Γ |- A ≅ A' : U] ->
@@ -170,7 +170,7 @@ Section Definitions.
170170 [Γ |- y ◃ A] ->
171171 [Γ |- tId A x y]
172172 | wfTypeUniv {Γ A} :
173- ~ isCanonical A ->
173+ ¬ isCanonical A ->
174174 [Γ |- A ▹h U] ->
175175 [Γ |- A]
176176 (** **** Type inference *)
@@ -179,16 +179,16 @@ Section Definitions.
179179 in_ctx Γ n decl ->
180180 [Γ |- tRel n ▹ decl]
181181 | infProd {Γ} {A B} :
182- [ Γ |- A ▹h U] ->
182+ [ Γ |- A ▹h U] ->
183183 [Γ ,, A |- B ▹h U ] ->
184184 [ Γ |- tProd A B ▹ U ]
185185 | infLam {Γ} {A B t} :
186186 [ Γ |- A] ->
187- [ Γ ,, A |- t ▹ B ] ->
187+ [ Γ ,, A |- t ▹ B ] ->
188188 [ Γ |- tLambda A t ▹ tProd A B]
189189 | infApp {Γ} {f a A B} :
190- [ Γ |- f ▹h tProd A B ] ->
191- [ Γ |- a ◃ A ] ->
190+ [ Γ |- f ▹h tProd A B ] ->
191+ [ Γ |- a ◃ A ] ->
192192 [ Γ |- tApp f a ▹ B[a..] ]
193193 | infNat {Γ} :
194194 [Γ |- tNat ▹ U]
@@ -210,11 +210,11 @@ Section Definitions.
210210 [Γ ,, tEmpty |- P ] ->
211211 [Γ |- tEmptyElim P e ▹ P[e..]]
212212 | infSig {Γ} {A B} :
213- [ Γ |- A ▹h U] ->
213+ [ Γ |- A ▹h U] ->
214214 [Γ ,, A |- B ▹h U ] ->
215215 [ Γ |- tSig A B ▹ U ]
216216 | infPair {Γ A B a b} :
217- [ Γ |- A] ->
217+ [ Γ |- A] ->
218218 [Γ ,, A |- B] ->
219219 [Γ |- a ◃ A] ->
220220 [Γ |- b ◃ B[a..]] ->
@@ -252,7 +252,7 @@ Section Definitions.
252252 (** **** Type-checking *)
253253 with CheckAlg : context -> term -> term -> Type :=
254254 | checkConv {Γ t A A'} :
255- [ Γ |- t ▹ A ] ->
255+ [ Γ |- t ▹ A ] ->
256256 conv_type Γ A A' ->
257257 [ Γ |- t ◃ A' ]
258258
@@ -303,11 +303,11 @@ with UConvRedAlg : term -> term -> Type :=
303303 [tLambda A t ≅h tLambda A' t']
304304 | LambNeUAlg {A t n'} :
305305 whne n' ->
306- [t ≅ eta_expand n'] ->
306+ [t ≅ eta_expand n'] ->
307307 [tLambda A t ≅h n']
308308 | NeLamUAlg {n A' t'} :
309309 whne n ->
310- [eta_expand n ≅ t'] ->
310+ [eta_expand n ≅ t'] ->
311311 [n ≅h tLambda A' t']
312312 | SigCongUAlg {A B A' B'} :
313313 [A ≅ A'] ->
@@ -423,13 +423,13 @@ End AlgorithmicTypedConvData.
423423
424424(** ** Induction principles *)
425425
426- (** Similarly to declarative typing, we need some massaging to turn the output of
426+ (** Similarly to declarative typing, we need some massaging to turn the output of
427427Scheme to something that fits our purpose, and we also define a function that computes
428428the conclusion of a proof by induction. *)
429429Section InductionPrinciples.
430430 Import AlgorithmicTypingData AlgorithmicTypedConvData.
431431
432- Scheme
432+ Scheme
433433 Minimality for ConvTypeAlg Sort Type with
434434 Minimality for ConvTypeRedAlg Sort Type with
435435 Minimality for ConvNeuAlg Sort Type with
@@ -514,7 +514,7 @@ Definition AlgoTypingInductionConcl :=
514514 exact t').
515515
516516
517- Scheme
517+ Scheme
518518Minimality for UConvAlg Sort Type with
519519Minimality for UConvRedAlg Sort Type with
520520Minimality for UConvNeuAlg Sort Type .
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