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Remove or make explicit dependency on coq.init.logic #234

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merged 5 commits into from
Mar 7, 2023
Merged

Remove or make explicit dependency on coq.init.logic #234

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659408f
Make TypeCat/General.v depend on Coq.Init.Logic.
m-lindgren Mar 5, 2023
f975b6d
Make Initiality/Interpretation.v depend on Coq.Init.Logic.
m-lindgren Mar 5, 2023
1f31e69
Remove dependency on Coq.Init.Logic.
m-lindgren Mar 5, 2023
4bf9b0f
Update Interpretation.v
m-lindgren Mar 5, 2023
54935d2
Update TypeTheory/TypeCat/General.v
m-lindgren Mar 5, 2023
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4 changes: 2 additions & 2 deletions TypeTheory/Csystems/hSet_ltowers.v
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Expand Up @@ -699,11 +699,11 @@ Proof.
exact eq.
}
clear eq0.
remember (transportf (isover X) (! eq) (isover_X_ftnX X (S n))) as H''.
set (H'' := transportf (isover X) (! eq) (isover_X_ftnX X (S n))).
set (H3 := transportf (isover X) (! eq') (isover_XX X)).
assert (eq'' : H'' = H3) by (apply isaprop_isover).
rewrite eq''.
clear HeqH'' H'' eq'' eq.
clear H'' eq'' eq.
induction eq'.
cbn in H3.
unfold H3.
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9 changes: 9 additions & 0 deletions TypeTheory/Initiality/Interpretation.v
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@@ -1,5 +1,14 @@
(** This file defines the interpretation function, from the syntax of our toy type theory into any split type-cat with suitable structure. *)


(** * NOTE: This file depends on Coq.Init.Logic.
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Removing the following line causes the error:

File "./TypeTheory/TypeTheory/Initiality/Interpretation.v", line 366, characters 4-5:
Error: [Focus] Wrong bullet -: Current bullet + is not finished.
*)
Require Import Coq.Init.Logic.

Require Import UniMath.MoreFoundations.All.
Require Import UniMath.CategoryTheory.Core.Prelude.

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2 changes: 1 addition & 1 deletion TypeTheory/Initiality/SyntacticCategory.v
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Expand Up @@ -287,7 +287,7 @@ Section Contexts_Modulo_Equality.
destruct ΓΓ as [n ΓΓ]. generalize ΓΓ.
apply setquotunivprop'.
{ intros; apply isapropishinh. }
intros Γ; apply hinhpr. exists Γ; auto.
intros Γ; apply hinhpr. exists Γ; apply idpath.
Defined.

End Contexts_Modulo_Equality.
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8 changes: 8 additions & 0 deletions TypeTheory/TypeCat/General.v
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Expand Up @@ -5,6 +5,14 @@ Note: much of this essentially duplicates material given already in the [CwF_Spl

Probably much of this really should belong in a different package. *)

(** * NOTE: This file depends on Coq.Init.Logic.
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Removing the following line causes the error:

File "./TypeTheory/TypeTheory/TypeCat/General.v", line 365, characters 6-115:
Error: not found in table: core.eq.type
*)
Require Import Coq.Init.Logic.

Require Import UniMath.MoreFoundations.All.
Require Import TypeTheory.Auxiliary.CategoryTheoryImports.

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20 changes: 10 additions & 10 deletions TypeTheory/TypeConstructions/CwF_SplitTypeCat_TypeEquiv.v
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Expand Up @@ -362,11 +362,11 @@ Lemma unit_equiv_inv1 : ∏ x : unit_structure Sc, unit_equiv_2(unit_equiv_1 x)
Proof.
intro Unit.
apply pair_path_in2.
assert (prj : pr2 Unit = pr12 Unit ,, pr22 Unit) by auto.
assert (prj : pr2 Unit = pr12 Unit ,, pr22 Unit) by apply idpath.
apply pathsinv0.
apply (pathscomp0 prj).
refine (subtypePairEquality' _ _ ).
- assert (func: pr12 Unit = λ Γ : C , pr12 Unit Γ) by auto.
- assert (func: pr12 Unit = λ Γ : C , pr12 Unit Γ) by apply idpath.
apply (pathscomp0 func).
apply funextsec2.
intro Γ.
Expand All @@ -378,11 +378,11 @@ Lemma unit_equiv_inv2 : ∏ x : CwF_unit_structure CWF, unit_equiv_1(unit_equiv_
Proof.
intro Unit.
apply pair_path_in2.
assert (prj : pr2 Unit = (pr12 Unit ,, pr22 Unit)) by auto.
assert (prj : pr2 Unit = (pr12 Unit ,, pr22 Unit)) by apply idpath.
apply pathsinv0.
apply (pathscomp0 prj).
refine (subtypePairEquality' _ _ ).
- assert (func: pr12 Unit = λ Γ : C , pr12 Unit Γ) by auto.
- assert (func: pr12 Unit = λ Γ : C , pr12 Unit Γ) by apply idpath.
apply (pathscomp0 func).
apply funextsec2.
intro Γ.
Expand Down Expand Up @@ -434,15 +434,15 @@ Lemma universe_equiv_inv1
Proof.
intro Universe.
apply pair_path_in2.
assert (prj : pr2 Universe = pr12 Universe ,, pr22 Universe) by auto.
assert (prj : pr2 Universe = pr12 Universe ,, pr22 Universe) by apply idpath.
apply pathsinv0.
apply (pathscomp0 prj).
refine (subtypePairEquality' _ _ ).
- assert (func : pr12 Universe = λ Γ : C , pr12 Universe Γ) by auto.
- assert (func : pr12 Universe = λ Γ : C , pr12 Universe Γ) by apply idpath.
apply (pathscomp0 func).
apply funextsec2.
intro Γ.
assert (simplman : pr12 Universe Γ = λ a : _, pr12 Universe Γ a) by auto.
assert (simplman : pr12 Universe Γ = λ a : _, pr12 Universe Γ a) by apply idpath.
rewrite simplman.
reflexivity.
- do 4 (apply impred_isaprop; intro); exact (pr12 Split _ _ _).
Expand All @@ -453,15 +453,15 @@ Lemma universe_equiv_inv2
Proof.
intro Universe.
apply pair_path_in2.
assert (prj : pr2 Universe = pr12 Universe ,, pr22 Universe) by auto.
assert (prj : pr2 Universe = pr12 Universe ,, pr22 Universe) by apply idpath.
apply pathsinv0.
apply (pathscomp0 prj).
refine (subtypePairEquality' _ _ ).
- assert (func : pr12 Universe = λ Γ : C , pr12 Universe Γ) by auto.
- assert (func : pr12 Universe = λ Γ : C , pr12 Universe Γ) by apply idpath.
apply (pathscomp0 func).
apply funextsec2.
intro Γ.
assert (simplman : pr12 Universe Γ = λ a : _, pr12 Universe Γ a) by auto.
assert (simplman : pr12 Universe Γ = λ a : _, pr12 Universe Γ a) by apply idpath.
rewrite simplman.
cbn; apply funextsec; intro a; rewrite tm_equiv_inter_21; reflexivity.
- do 4 (apply impred_isaprop; intro); exact (setproperty (Ty CWF _) _ _).
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