Metamath Proof Explorer


Theorem k0004ss1

Description: The topological simplex of dimension N is a subset of the real vectors of dimension ( N + 1 ) . (Contributed by RP, 29-Mar-2021)

Ref Expression
Hypothesis k0004.a A=n0t011n+1|k=1n+1tk=1
Assertion k0004ss1 N0AN1N+1

Proof

Step Hyp Ref Expression
1 k0004.a A=n0t011n+1|k=1n+1tk=1
2 1 k0004val N0AN=t011N+1|k=1N+1tk=1
3 simp2 N0t011N+1k=1N+1tk=1t011N+1
4 3 rabssdv N0t011N+1|k=1N+1tk=1011N+1
5 2 4 eqsstrd N0AN011N+1
6 reex V
7 unitssre 01
8 mapss V01011N+11N+1
9 6 7 8 mp2an 011N+11N+1
10 5 9 sstrdi N0AN1N+1