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feat(library/algebra/group.lean): add coercions from additive (comm) monoid to (comm) monoid

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This commit is contained in:
Jeremy Avigad 2015-05-16 18:27:49 +10:00
parent 63bb4b558a
commit 87e4f7a951
1 changed files with 15 additions and 0 deletions
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library/algebra/group.lean
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@ -136,6 +136,21 @@ theorem add_zero [s : add_monoid A] (a : A) : a + 0 = a := !add_monoid.add_zero
structure add_comm_monoid [class] (A : Type) extends add_monoid A, add_comm_semigroup A structure add_comm_monoid [class] (A : Type) extends add_monoid A, add_comm_semigroup A
definition add_monoid.to_monoid {A : Type} [s : add_monoid A] : monoid A :=
⦃ monoid,
mul := add_monoid.add,
mul_assoc := add_monoid.add_assoc,
one := add_monoid.zero A,
mul_one := add_monoid.add_zero,
one_mul := add_monoid.zero_add
⦄
definition add_comm_monoid.to_comm_monoid {A : Type} [s : add_comm_monoid A] : comm_monoid A :=
⦃ comm_monoid,
add_monoid.to_monoid,
mul_comm := add_comm_monoid.add_comm
⦄
/- group -/ /- group -/
structure group [class] (A : Type) extends monoid A, has_inv A := structure group [class] (A : Type) extends monoid A, has_inv A :=