Metamath Proof Explorer


Definition df-ee

Description: Define the Euclidean space generator. For details, see elee . (Contributed by Scott Fenton, 3-Jun-2013)

Ref Expression
Assertion df-ee 𝔼 = ( 𝑛 ∈ ℕ ↦ ( ℝ ↑m ( 1 ... 𝑛 ) ) )

Detailed syntax breakdown

Step Hyp Ref Expression
0 cee ⊢ 𝔼
1 vn ⊢ 𝑛
2 cn ⊢ ℕ
3 cr ⊢ ℝ
4 cmap ⊢ ↑m
5 c1 ⊢ 1
6 cfz ⊢ ...
7 1 cv ⊢ 𝑛
8 5 7 6 co ⊢ ( 1 ... 𝑛 )
9 3 8 4 co ⊢ ( ℝ ↑m ( 1 ... 𝑛 ) )
10 1 2 9 cmpt ⊢ ( 𝑛 ∈ ℕ ↦ ( ℝ ↑m ( 1 ... 𝑛 ) ) )
11 0 10 wceq ⊢ 𝔼 = ( 𝑛 ∈ ℕ ↦ ( ℝ ↑m ( 1 ... 𝑛 ) ) )