Database
BASIC LINEAR ALGEBRA
Abstract multivariate polynomials
Definition and basic properties
opsrmulr
Metamath Proof Explorer
Description: The multiplication operation of the ordered power series structure.
(Contributed by Mario Carneiro , 8-Feb-2015) (Revised by Mario
Carneiro , 30-Aug-2015)
Ref
Expression
Hypotheses
opsrbas.s
⊢ S = I mPwSer R
opsrbas.o
⊢ O = I ordPwSer R ⁡ T
opsrbas.t
⊢ φ → T ⊆ I × I
Assertion
opsrmulr
⊢ φ → ⋅ S = ⋅ O
Proof
Step
Hyp
Ref
Expression
1
opsrbas.s
⊢ S = I mPwSer R
2
opsrbas.o
⊢ O = I ordPwSer R ⁡ T
3
opsrbas.t
⊢ φ → T ⊆ I × I
4
df-mulr
⊢ ⋅ 𝑟 = Slot 3
5
3nn
⊢ 3 ∈ ℕ
6
3lt10
⊢ 3 < 10
7
1 2 3 4 5 6
opsrbaslem
⊢ φ → ⋅ S = ⋅ O