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refactor(library/algebra/ring): add alternate names for dvd.intro, dvd.intro_left

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Jeremy Avigad 2015-08-09 21:23:44 -04:00
parent 209d7b07aa
commit eca3437388
1 changed files with 4 additions and 0 deletions
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library/algebra/ring.lean
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@ -78,9 +78,13 @@ section comm_semiring
theorem dvd.intro {a b c : A} (H : a * c = b) : a ∣ b := theorem dvd.intro {a b c : A} (H : a * c = b) : a ∣ b :=
exists.intro _ H⁻¹ exists.intro _ H⁻¹
theorem dvd_of_mul_right_eq {a b c : A} (H : a * c = b) : a ∣ b := dvd.intro H
theorem dvd.intro_left {a b c : A} (H : c * a = b) : a ∣ b := theorem dvd.intro_left {a b c : A} (H : c * a = b) : a ∣ b :=
dvd.intro (!mul.comm ▸ H) dvd.intro (!mul.comm ▸ H)
theorem dvd_of_mul_left_eq {a b c : A} (H : c * a = b) : a ∣ b := dvd.intro_left H
theorem exists_eq_mul_right_of_dvd {a b : A} (H : a ∣ b) : ∃c, b = a * c := H theorem exists_eq_mul_right_of_dvd {a b : A} (H : a ∣ b) : ∃c, b = a * c := H
theorem dvd.elim {P : Prop} {a b : A} (H₁ : a ∣ b) (H₂ : ∀c, b = a * c → P) : P := theorem dvd.elim {P : Prop} {a b : A} (H₁ : a ∣ b) (H₂ : ∀c, b = a * c → P) : P :=