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	, , , , ,  ⊢
	: , : , :
1	theorem		⊢
	proveit.logic.equality.sub_left_side_into
2	instantiation	4, 5, 16, 6	, , , , ,  ⊢
	: , : , : , :
3	instantiation	7, 8, 9, 10	, , , , ,  ⊢
	: , : , : , :
4	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
5	instantiation	11, 22, 23, 32	⊢
	: , : , :
6	instantiation	12, 13, 14	, , , ,  ⊢
	: , : , :
7	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
8	instantiation	15, 16, 59, 30, 31, 32, 17, 34, 35, 36, 37	, , , , ,  ⊢
	: , : , : , : , : , : , : , : , : , :
9	instantiation	18	⊢
	:
10	instantiation	19, 20	, , , ,  ⊢
	: , :
11	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
12	theorem		⊢
	proveit.logic.equality.sub_right_side_into
13	instantiation	21, 22, 23, 32, 24, 34, 35, 36, 37	, , , ,  ⊢
	: , : , : , :
14	instantiation	25, 30, 59, 31, 32, 33, 34, 35, 36, 37	, , , ,  ⊢
	: , : , : , : , : , : , : , : , : , :
15	theorem		⊢
	proveit.linear_algebra.tensors.factor_scalar_from_tensor_prod
16	assumption		⊢
17	instantiation	40	⊢
	: , :
18	axiom		⊢
	proveit.logic.equality.equals_reflexivity
19	theorem		⊢
	proveit.logic.equality.equals_reversal
20	instantiation	26, 27	, , , ,  ⊢
	: , : , :
21	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
22	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
23	instantiation	28	⊢
	: , : , : , :
24	instantiation	28	⊢
	: , : , : , :
25	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_association
26	axiom		⊢
	proveit.logic.equality.substitution
27	instantiation	29, 30, 59, 31, 32, 33, 34, 35, 36, 37	, , , ,  ⊢
	: , : , : , : , : , : , : , : , : , :
28	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
29	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_disassociation
30	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
31	instantiation	40	⊢
	: , :
32	instantiation	38, 39	⊢
	:
33	instantiation	40	⊢
	: , :
34	assumption		⊢
35	assumption		⊢
36	instantiation	41, 42	,  ⊢
	:
37	assumption		⊢
38	theorem		⊢
	proveit.linear_algebra.real_vec_set_is_vec_space
39	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
40	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
41	assumption		⊢
42	instantiation	43, 44, 45	⊢
	:
43	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
44	instantiation	60, 46, 58	⊢
	: , : , :
45	instantiation	47, 48	⊢
	: , :
46	instantiation	49, 56, 57	⊢
	: , :
47	theorem		⊢
	proveit.numbers.ordering.relax_less
48	instantiation	50, 51, 52	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
50	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
51	instantiation	53, 54	⊢
	:
52	instantiation	55, 56, 57, 58	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
54	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
55	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
56	instantiation	60, 61, 59	⊢
	: , : , :
57	instantiation	60, 61, 62	⊢
	: , : , :
58	assumption		⊢
59	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
60	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
61	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
62	theorem		⊢
	proveit.numbers.numerals.decimals.nat4