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, 10*	, , , , , ,  ⊢
	: , : , : , : , : , : , : , : , : , :
1	reference	21	⊢
2	reference	29	⊢
3	reference	35	⊢
4	reference	37	⊢
5	reference	39	⊢
6	reference	40	⊢
7	reference	22	⊢
8	reference	42	⊢
9	instantiation	11, 22, 30, 23	, , , ,  ⊢
	: , : , : , :
10	instantiation	12, 13, 14	, , , , , ,  ⊢
	: , : , :
11	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
12	axiom		⊢
	proveit.logic.equality.equals_transitivity
13	instantiation	15, 16	, , , , ,  ⊢
	: , : , :
14	instantiation	17, 18, 19, 29, 30, 20*	, , , , , ,  ⊢
	: , : , : , : , :
15	axiom		⊢
	proveit.logic.equality.substitution
16	instantiation	21, 30, 35, 37, 39, 40, 22, 42, 23, 24*	, , , , ,  ⊢
	: , : , : , : , : , : , : , : , : , :
17	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.doubly_scaled_as_singly_scaled
18	instantiation	31, 25, 26, 40	⊢
	: , : , :
19	instantiation	32, 25, 26, 40, 27, 42, 43, 44, 45, 46	, , , ,  ⊢
	: , : , : , :
20	instantiation	28, 29, 30	,  ⊢
	: , :
21	theorem		⊢
	proveit.linear_algebra.tensors.factor_scalar_from_tensor_prod
22	instantiation	31, 33, 38, 40	⊢
	: , : , :
23	instantiation	32, 33, 38, 40, 41, 43, 44, 45, 46	, , ,  ⊢
	: , : , : , :
24	instantiation	34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46	, , , ,  ⊢
	: , : , : , : , : , : , : , : , : , :
25	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
26	instantiation	47	⊢
	: , : , : , : , :
27	instantiation	47	⊢
	: , : , : , : , :
28	axiom		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult
29	instantiation	48, 63, 49	⊢
	: , : , :
30	assumption		⊢
31	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
32	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
33	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
34	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_disassociation
35	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
36	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
37	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
38	instantiation	51	⊢
	: , : , : , :
39	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
40	instantiation	50, 60	⊢
	:
41	instantiation	51	⊢
	: , : , : , :
42	instantiation	56, 57, 52	⊢
	: , : , :
43	instantiation	56, 57, 53	⊢
	: , : , :
44	instantiation	56, 57, 54	⊢
	: , : , :
45	instantiation	56, 57, 55	⊢
	: , : , :
46	instantiation	56, 57, 58	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_5_typical_eq
48	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
49	assumption		⊢
50	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
51	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
52	assumption		⊢
53	assumption		⊢
54	assumption		⊢
55	assumption		⊢
56	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
57	instantiation	59, 60, 61	⊢
	: , : , :
58	assumption		⊢
59	theorem		⊢
	proveit.logic.sets.cartesian_products.cart_exp_subset_eq
60	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
61	instantiation	62, 63	⊢
	: , :
62	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
63	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
*equality replacement requirements