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Matrix: use strip_reflections to avoid extra universe variables #2130

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jdchristensen merged 1 commit into from
Nov 7, 2024
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Matrix: use strip_reflections to avoid extra universe variables #2130

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14 changes: 8 additions & 6 deletions theories/Algebra/Rings/Matrix.v
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Original file line number Diff line number Diff line change
Expand Up @@ -5,6 +5,7 @@ Require Import Algebra.Rings.Ring Algebra.Rings.Module Algebra.Rings.CRing
Algebra.Rings.KroneckerDelta Algebra.Rings.Vector.
Require Import abstract_algebra.
Require Import WildCat.Core WildCat.Paths.
Require Import Modalities.ReflectiveSubuniverse.

Set Universe Minimization ToSet.

Expand Down Expand Up @@ -692,12 +693,13 @@ Proof.
Defined.

(** The sum of two upper triangular matrices is upper triangular. *)
Global Instance upper_triangular_plus {R : Ring@{i}} {n : nat} (M N : Matrix R n n)
Global Instance upper_triangular_plus@{i} {R : Ring@{i}} {n : nat} (M N : Matrix R n n)
{H1 : IsUpperTriangular M} {H2 : IsUpperTriangular N}
: IsUpperTriangular (matrix_plus M N).
Proof.
unfold IsUpperTriangular.
strip_truncations; apply tr.
(* We use [strip_reflections] rather than [strip_truncations] here and below because it generates fewer universe variables in some versions of Coq. *)
strip_reflections; apply tr.
intros i j Hi Hj lt_i_j.
specialize (H1 i j Hi Hj lt_i_j).
specialize (H2 i j Hi Hj lt_i_j).
Expand All @@ -718,12 +720,12 @@ Proof.
Defined.

(** The negation of an upper triangular matrix is upper triangular. *)
Global Instance upper_triangular_negate {R : Ring@{i}} {n : nat} (M : Matrix R n n)
Global Instance upper_triangular_negate@{i} {R : Ring@{i}} {n : nat} (M : Matrix R n n)
{H : IsUpperTriangular M}
: IsUpperTriangular (matrix_negate M).
Proof.
unfold IsUpperTriangular.
strip_truncations; apply tr.
strip_reflections; apply tr.
intros i j Hi Hj lt_i_j.
rewrite entry_Build_Matrix.
rewrite <- rng_negate_zero; f_ap.
Expand All @@ -741,12 +743,12 @@ Proof.
Defined.

(** The product of two upper triangular matrices is upper triangular. *)
Global Instance upper_triangular_mult {R : Ring@{i}} {n : nat}
Global Instance upper_triangular_mult@{i} {R : Ring@{i}} {n : nat}
(M N : Matrix R n n) {H1 : IsUpperTriangular M} {H2 : IsUpperTriangular N}
: IsUpperTriangular (matrix_mult M N).
Proof.
unfold IsUpperTriangular.
strip_truncations; apply tr.
strip_reflections; apply tr.
intros i j Hi Hj lt_i_j.
rewrite entry_Build_Matrix.
apply ab_sum_zero.
Expand Down