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