Skip to content
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

Jump to bottom

[Merged by Bors] - feat(data/polynomial/degree/lemmas): add some lemmas and rename some lemmas #13235

Closed
wants to merge 1 commit into from
Closed

[Merged by Bors] - feat(data/polynomial/degree/lemmas): add some lemmas and rename some lemmas #13235

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
28 changes: 12 additions & 16 deletions src/data/polynomial/degree/lemmas.lean
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -95,8 +95,6 @@ le_antisymm (nat_degree_mul_C_le p a) (calc

/-- Although not explicitly stated, the assumptions of lemma `nat_degree_mul_C_eq_of_mul_ne_zero`
force the polynomial `p` to be non-zero, via `p.leading_coeff ≠ 0`.
Lemma `nat_degree_mul_C_eq_of_no_zero_divisors` below separates cases, in order to overcome this
hurdle.
-/
lemma nat_degree_mul_C_eq_of_mul_ne_zero (h : p.leading_coeff * a ≠ 0) :
(p * C a).nat_degree = p.nat_degree :=
Expand All @@ -108,8 +106,6 @@ end

/-- Although not explicitly stated, the assumptions of lemma `nat_degree_C_mul_eq_of_mul_ne_zero`
force the polynomial `p` to be non-zero, via `p.leading_coeff ≠ 0`.
Lemma `nat_degree_C_mul_eq_of_no_zero_divisors` below separates cases, in order to overcome this
hurdle.
-/
lemma nat_degree_C_mul_eq_of_mul_ne_zero (h : a * p.leading_coeff ≠ 0) :
(C a * p).nat_degree = p.nat_degree :=
Expand Down Expand Up @@ -217,21 +213,21 @@ end semiring
section no_zero_divisors
variables [semiring R] [no_zero_divisors R] {p q : R[X]}

lemma nat_degree_mul_C_eq_of_no_zero_divisors (a0 : a ≠ 0) :
lemma degree_mul_C (a0 : a ≠ 0) :
(p * C a).degree = p.degree :=
by rw [degree_mul, degree_C a0, add_zero]

lemma degree_C_mul (a0 : a ≠ 0) :
(C a * p).degree = p.degree :=
by rw [degree_mul, degree_C a0, zero_add]

lemma nat_degree_mul_C (a0 : a ≠ 0) :
(p * C a).nat_degree = p.nat_degree :=
begin
by_cases p0 : p = 0,
{ rw [p0, zero_mul] },
{ exact nat_degree_mul_C_eq_of_mul_ne_zero (mul_ne_zero (leading_coeff_ne_zero.mpr p0) a0) }
end
by simp only [nat_degree, degree_mul_C a0]

lemma nat_degree_C_mul_eq_of_no_zero_divisors (a0 : a ≠ 0) :
lemma nat_degree_C_mul (a0 : a ≠ 0) :
(C a * p).nat_degree = p.nat_degree :=
begin
by_cases p0 : p = 0,
{ rw [p0, mul_zero] },
{ exact nat_degree_C_mul_eq_of_mul_ne_zero (mul_ne_zero a0 (leading_coeff_ne_zero.mpr p0)) }
end
by simp only [nat_degree, degree_C_mul a0]

lemma nat_degree_comp : nat_degree (p.comp q) = nat_degree p * nat_degree q :=
begin
Expand Down