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	, , , ,  ⊢
	: , :
1	theorem		⊢
	proveit.logic.equality.equals_reversal
2	modus ponens	3, 4	, , , ,  ⊢
3	instantiation	5, 27, 6, 12	⊢
	: , : , : , : , : , : , : , : , : , : , :
4	generalization	7	, , , ,  ⊢
5	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_distribution_over_summation_with_scalar_mult
6	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
7	instantiation	8, 9, 10	, , , , ,  ⊢
	: , : , :
8	theorem		⊢
	proveit.logic.equality.sub_left_side_into
9	instantiation	11, 12, 15, 13	, , , , ,  ⊢
	: , : , : , :
10	instantiation	14, 15, 27, 29, 16, 31, 17, 34	, , , , ,  ⊢
	: , : , : , : , : , : , : , : , : , :
11	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
12	instantiation	21, 23, 24, 29	⊢
	: , : , :
13	instantiation	18, 19, 20	, , , ,  ⊢
	: , : , :
14	theorem		⊢
	proveit.linear_algebra.tensors.factor_scalar_from_tensor_prod
15	assumption		⊢
16	instantiation	21, 52, 28, 29	⊢
	: , : , :
17	instantiation	22, 52, 28, 29, 30, 32, 33	, ,  ⊢
	: , : , : , :
18	theorem		⊢
	proveit.logic.equality.sub_right_side_into
19	instantiation	22, 23, 24, 29, 25, 31, 32, 33, 34	, , , ,  ⊢
	: , : , : , :
20	instantiation	26, 27, 57, 28, 29, 30, 31, 32, 33, 34	, , , ,  ⊢
	: , : , : , : , : , : , : , : , : , :
21	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
22	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
23	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
24	instantiation	35	⊢
	: , : , : , :
25	instantiation	35	⊢
	: , : , : , :
26	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_association
27	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
28	instantiation	38	⊢
	: , :
29	instantiation	36, 37	⊢
	:
30	instantiation	38	⊢
	: , :
31	assumption		⊢
32	assumption		⊢
33	instantiation	39, 40	,  ⊢
	:
34	assumption		⊢
35	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
36	theorem		⊢
	proveit.linear_algebra.real_vec_set_is_vec_space
37	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
38	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
39	assumption		⊢
40	instantiation	41, 42, 43	⊢
	:
41	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
42	instantiation	58, 44, 56	⊢
	: , : , :
43	instantiation	45, 46	⊢
	: , :
44	instantiation	47, 54, 55	⊢
	: , :
45	theorem		⊢
	proveit.numbers.ordering.relax_less
46	instantiation	48, 49, 50	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
48	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
49	instantiation	51, 52	⊢
	:
50	instantiation	53, 54, 55, 56	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
52	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
53	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
54	instantiation	58, 59, 57	⊢
	: , : , :
55	instantiation	58, 59, 60	⊢
	: , : , :
56	assumption		⊢
57	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
58	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
59	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
60	theorem		⊢
	proveit.numbers.numerals.decimals.nat4