Skip to content

Add support for latest version of math-comp algebra and analysis #124

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Open
lyonel2017 wants to merge 1 commit into
base: main
Choose a base branch
from
Open

Add support for latest version of math-comp algebra and analysis #124

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
22 changes: 11 additions & 11 deletions theories/Crypt/examples/PolynomialUtils.v
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -499,16 +499,16 @@ Proof.
by rewrite (y_in_zero_points Hin).
Qed.

Definition head_poly {R: ringType} (q: {poly R}): R := q`_0.
Definition tail_poly {R: ringType} (q: {poly R}): {poly R} := Poly (behead q).
Definition head_poly {R: nzRingType} (q: {poly R}): R := q`_0.
Definition tail_poly {R: nzRingType} (q: {poly R}): {poly R} := Poly (behead q).

Lemma head_cons_poly {R: ringType} (a: R) (q: {poly R}):
Lemma head_cons_poly {R: nzRingType} (a: R) (q: {poly R}):
head_poly (cons_poly a q) = a.
Proof.
by rewrite /head_poly coef_cons.
Qed.

Lemma tail_cons_poly {R: ringType} (a: R) (q: {poly R}):
Lemma tail_cons_poly {R: nzRingType} (a: R) (q: {poly R}):
tail_poly (cons_poly a q) = q.
Proof.
rewrite /tail_poly polyseq_cons.
Expand All @@ -519,7 +519,7 @@ Proof.
by case: (a != 0).
Qed.

Lemma size_tail_poly {R: ringType} (q: {poly R}):
Lemma size_tail_poly {R: nzRingType} (q: {poly R}):
size (tail_poly q) = (size q).-1.
Proof.
rewrite /tail_poly.
Expand All @@ -528,14 +528,14 @@ Proof.
- by rewrite (PolyK Hs).
Qed.

Lemma last_neq_0 {R: ringType} (a: R) (s: seq R):
Lemma last_neq_0 {R: nzRingType} (a: R) (s: seq R):
(last a s != 0 -> last 1 s != 0).
Proof.
case: s => H //=.
by apply: GRing.oner_neq0.
Qed.

Lemma cons_head_tail_poly {R: ringType} (q: {poly R}):
Lemma cons_head_tail_poly {R: nzRingType} (q: {poly R}):
cons_poly (head_poly q) (tail_poly q) = q.
Proof.
apply: poly_inj.
Expand All @@ -547,7 +547,7 @@ Proof.
by rewrite polyseqC Hs.
Qed.

Lemma cons_eq_head_tail_poly {R: ringType} (a: R) (q: {poly R}):
Lemma cons_eq_head_tail_poly {R: nzRingType} (a: R) (q: {poly R}):
a = head_poly q ->
cons_poly a (tail_poly q) = q.
Proof.
Expand All @@ -562,7 +562,7 @@ Qed.
Used to prove how [tail_poly] and [cons_poly] behaves when added
and negated.
*)
Lemma coef_poly_eq {R: ringType} (q1 q2: {poly R}):
Lemma coef_poly_eq {R: nzRingType} (q1 q2: {poly R}):
(forall i, q1`_i = q2`_i) <-> q1 = q2.
Proof.
split=> H.
Expand All @@ -589,14 +589,14 @@ Proof.
+ by apply: Hs2.
Qed.

Lemma tail_poly_add {R: ringType} (q1 q2: {poly R}):
Lemma tail_poly_add {R: nzRingType} (q1 q2: {poly R}):
tail_poly (q1 + q2) = tail_poly q1 + tail_poly q2.
Proof.
apply/coef_poly_eq; move => i.
by rewrite coefD !coef_Poly !nth_behead coefD.
Qed.

Lemma cons_poly_add {R: ringType} (m m': R) (q1 q2: {poly R}):
Lemma cons_poly_add {R: nzRingType} (m m': R) (q1 q2: {poly R}):
(cons_poly m' (q1 + q2) = (cons_poly m q1) + cons_poly (m'-m) q2)%R.
Proof.
apply/coef_poly_eq; move => i.
Expand Down
2 changes: 1 addition & 1 deletion theories/Crypt/nominal/Pr.v
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -208,7 +208,7 @@ Section LosslessCodeLemmas.
1: intros x; apply summable_mu_wgtd; intros y.
1: apply /andP; split; [ done | apply le1_mu1 ].
1: eapply eq_summable.
1: intros x; rewrite -dletE; reflexivity.
1: intros x; simpl; rewrite -dletE; reflexivity.
1: apply summable_mu.
rewrite -H.
apply eq_psum => x.
Expand Down
Loading