Metamath Proof Explorer


Definition df-ehl

Description: Define a function generating the real Euclidean spaces of finite dimension. The case n = 0 corresponds to a space of dimension 0, that is, limited to a neutral element (see ehl0 ). Members of this family of spaces are Hilbert spaces, as shown in - ehlhl . (Contributed by Thierry Arnoux, 16-Jun-2019)

Ref Expression
Assertion df-ehl 𝔼 hil = n 0 1 n

Detailed syntax breakdown

Step Hyp Ref Expression
0 cehl class 𝔼 hil
1 vn setvar n
2 cn0 class 0
3 crrx class ℝ↑
4 c1 class 1
5 cfz class
6 1 cv setvar n
7 4 6 5 co class 1 n
8 7 3 cfv class 1 n
9 1 2 8 cmpt class n 0 1 n
10 0 9 wceq wff 𝔼 hil = n 0 1 n