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(algebra/ring): ite_mul_one and ite_mul_zero_... #3217

Closed
wants to merge 2 commits into from
Closed

[Merged by Bors] - feat(algebra/ring): ite_mul_one and ite_mul_zero_... #3217

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
2 commits
Select commit Hold shift + click to select a range
4dc31ba
feat(algebra/ring): ite_mul_one and ite_mul_zero_...
semorrison Jun 28, 2020
f32f222
move lemma
semorrison Jun 29, 2020
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Jump to
Jump to file
Failed to load files.
Diff view
Diff view
10 changes: 10 additions & 0 deletions src/algebra/group/basic.lean
View file
Open in desktop
Expand Up @@ -11,6 +11,16 @@ import tactic.protected

universe u

section monoid
variables {M : Type u} [monoid M]

@[to_additive]
lemma ite_mul_one {P : Prop} [decidable P] {a b : M} :
ite P (a * b) 1 = ite P a 1 * ite P b 1 :=
by { by_cases h : P; simp [h], }

end monoid

section comm_semigroup
variables {G : Type u} [comm_semigroup G]

Expand Down
8 changes: 8 additions & 0 deletions src/algebra/ring.lean
View file
Open in desktop
Expand Up @@ -158,6 +158,14 @@ by simp
(if P then 1 else 0) * a = if P then a else 0 :=
by simp

lemma ite_mul_zero_left {α : Type*} [mul_zero_class α] (P : Prop) [decidable P] (a b : α) :
ite P (a * b) 0 = ite P a 0 * b :=
by { by_cases h : P; simp [h], }

lemma ite_mul_zero_right {α : Type*} [mul_zero_class α] (P : Prop) [decidable P] (a b : α) :
ite P (a * b) 0 = a * ite P b 0 :=
by { by_cases h : P; simp [h], }

variable (α)

/-- Either zero and one are nonequal in a semiring, or the semiring is the zero ring. -/
Expand Down