Metamath Proof Explorer


Theorem rlmds

Description: Metric component of the ring module. (Contributed by Mario Carneiro, 6-Oct-2015)

Ref Expression
Assertion rlmds dist R = dist ringLMod R

Proof

Step Hyp Ref Expression
1 rlmval ringLMod R = subringAlg R Base R
2 1 a1i ringLMod R = subringAlg R Base R
3 ssidd Base R Base R
4 2 3 srads dist R = dist ringLMod R
5 4 mptru dist R = dist ringLMod R