Show the Proof

import proveit
# Automation is not needed when only showing a stored proof:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%show_proof

	step type	requirements	statement
0	instantiation	1, 2, 3, 4, 5, 6, 7, 8	, , , ,  ⊢
	: , : , : , :
1	reference	21	⊢
2	reference	22	⊢
3	instantiation	30	⊢
	: , :
4	reference	24	⊢
5	reference	10	⊢
6	instantiation	30	⊢
	: , :
7	assumption		⊢
8	instantiation	9, 29, 10, 11, 12, 13, 14	, , ,  ⊢
	: , : , : , :
9	theorem		⊢
	proveit.linear_algebra.addition.closure
10	instantiation	15, 22, 23, 24	⊢
	: , : , :
11	instantiation	16	⊢
	: , : , :
12	instantiation	21, 22, 23, 24, 17, 26, 18	,  ⊢
	: , : , : , :
13	instantiation	21, 22, 23, 24, 19, 26, 20	,  ⊢
	: , : , : , :
14	instantiation	21, 22, 23, 24, 25, 26, 27	,  ⊢
	: , : , : , :
15	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
16	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
17	instantiation	30	⊢
	: , :
18	assumption		⊢
19	instantiation	30	⊢
	: , :
20	assumption		⊢
21	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
22	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
23	instantiation	30	⊢
	: , :
24	instantiation	28, 29	⊢
	:
25	instantiation	30	⊢
	: , :
26	assumption		⊢
27	assumption		⊢
28	theorem		⊢
	proveit.linear_algebra.real_vec_set_is_vec_space
29	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
30	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq