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*	, , , ,  ⊢
	: , : , : , : , :
1	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.doubly_scaled_as_singly_scaled
2	instantiation	7, 9, 10, 11	⊢
	: , : , :
3	instantiation	8, 9, 10, 11, 12, 13, 14	,  ⊢
	: , : , : , :
4	reference	16	,  ⊢
5	reference	31	,  ⊢
6	instantiation	15, 16, 31, 17*	, ,  ⊢
	: , :
7	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
8	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
9	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
10	instantiation	43	⊢
	: , :
11	instantiation	18, 28	⊢
	:
12	instantiation	43	⊢
	: , :
13	instantiation	20, 21, 19	⊢
	: , : , :
14	instantiation	20, 21, 22	⊢
	: , : , :
15	axiom		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult
16	instantiation	64, 46, 23	,  ⊢
	: , : , :
17	instantiation	24, 25, 26	, ,  ⊢
	: , : , :
18	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
19	assumption		⊢
20	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
21	instantiation	27, 28, 29	⊢
	: , : , :
22	assumption		⊢
23	instantiation	30, 44, 49	,  ⊢
	: , :
24	axiom		⊢
	proveit.logic.equality.equals_transitivity
25	instantiation	32, 33, 63, 59, 36, 34, 37, 38, 31	, ,  ⊢
	: , : , : , : , : , :
26	instantiation	32, 63, 33, 34, 35, 36, 37, 38, 41, 42	, ,  ⊢
	: , : , : , : , : , :
27	theorem		⊢
	proveit.logic.sets.cartesian_products.cart_exp_subset_eq
28	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
29	instantiation	39, 46	⊢
	: , :
30	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
31	instantiation	40, 41, 42	,  ⊢
	: , :
32	theorem		⊢
	proveit.numbers.multiplication.disassociation
33	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
34	instantiation	43	⊢
	: , :
35	instantiation	43	⊢
	: , :
36	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
37	instantiation	64, 46, 44	⊢
	: , : , :
38	instantiation	64, 46, 49	⊢
	: , : , :
39	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
40	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
41	instantiation	64, 46, 45	⊢
	: , : , :
42	instantiation	64, 46, 47	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
44	assumption		⊢
45	assumption		⊢
46	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
47	instantiation	48, 49, 50	⊢
	: , :
48	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
49	instantiation	64, 52, 51	⊢
	: , : , :
50	instantiation	64, 52, 53	⊢
	: , : , :
51	instantiation	64, 55, 54	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
53	instantiation	64, 55, 56	⊢
	: , : , :
54	instantiation	64, 57, 58	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
56	instantiation	64, 65, 59	⊢
	: , : , :
57	instantiation	60, 61, 62	⊢
	: , :
58	assumption		⊢
59	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
60	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
61	instantiation	64, 65, 63	⊢
	: , : , :
62	instantiation	64, 65, 66	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
64	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
65	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
66	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
*equality replacement requirements