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, 9*	, , , ,  ⊢
	: , : , : , :
1	reference	28	⊢
2	reference	29	⊢
3	instantiation	38	⊢
	: , :
4	reference	31	⊢
5	reference	12	⊢
6	instantiation	38	⊢
	: , :
7	instantiation	40, 41, 10	⊢
	: , : , :
8	instantiation	11, 44, 12, 13, 14, 15, 16	, , ,  ⊢
	: , : , : , :
9	instantiation	17, 18, 19, 20, 30, 21, 31	⊢
	: , : , : , : , : , : , :
10	assumption		⊢
11	theorem		⊢
	proveit.linear_algebra.addition.closure
12	instantiation	22, 29, 30, 31	⊢
	: , : , :
13	instantiation	23	⊢
	: , : , :
14	instantiation	28, 29, 30, 31, 24, 33, 25	,  ⊢
	: , : , : , :
15	instantiation	28, 29, 30, 31, 26, 33, 27	,  ⊢
	: , : , : , :
16	instantiation	28, 29, 30, 31, 32, 33, 34	,  ⊢
	: , : , : , :
17	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_vec_space_disassociation
18	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
19	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
20	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
21	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
22	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
23	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
24	instantiation	38	⊢
	: , :
25	instantiation	40, 41, 35	⊢
	: , : , :
26	instantiation	38	⊢
	: , :
27	instantiation	40, 41, 36	⊢
	: , : , :
28	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
29	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
30	instantiation	38	⊢
	: , :
31	instantiation	37, 44	⊢
	:
32	instantiation	38	⊢
	: , :
33	instantiation	40, 41, 39	⊢
	: , : , :
34	instantiation	40, 41, 42	⊢
	: , : , :
35	assumption		⊢
36	assumption		⊢
37	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
38	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
39	assumption		⊢
40	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
41	instantiation	43, 44, 45	⊢
	: , : , :
42	assumption		⊢
43	theorem		⊢
	proveit.logic.sets.cartesian_products.cart_exp_subset_eq
44	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
45	instantiation	46, 47	⊢
	: , :
46	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
47	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
*equality replacement requirements