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	modus ponens	1, 2	, , , ,  ⊢
1	instantiation	3, 64, 4, 35, 10, 22	⊢
	: , : , : , : , : , : , : , : , : , : , :
2	generalization	5	, , , ,  ⊢
3	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_distribution_over_summation_with_scalar_mult
4	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
5	instantiation	6, 7, 8	, , , , ,  ⊢
	: , : , :
6	theorem		⊢
	proveit.logic.equality.sub_left_side_into
7	instantiation	9, 10, 21, 11	, , , , ,  ⊢
	: , : , : , :
8	instantiation	12, 13, 14, 15	, , , , ,  ⊢
	: , : , : , :
9	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
10	instantiation	16, 27, 28, 37	⊢
	: , : , :
11	instantiation	17, 18, 19	, , , ,  ⊢
	: , : , :
12	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
13	instantiation	20, 21, 64, 35, 36, 37, 22, 39, 40, 41, 42	, , , , ,  ⊢
	: , : , : , : , : , : , : , : , : , :
14	instantiation	23	⊢
	:
15	instantiation	24, 25	, , , ,  ⊢
	: , :
16	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
17	theorem		⊢
	proveit.logic.equality.sub_right_side_into
18	instantiation	26, 27, 28, 37, 29, 39, 40, 41, 42	, , , ,  ⊢
	: , : , : , :
19	instantiation	30, 35, 64, 36, 37, 38, 39, 40, 41, 42	, , , ,  ⊢
	: , : , : , : , : , : , : , : , : , :
20	theorem		⊢
	proveit.linear_algebra.tensors.factor_scalar_from_tensor_prod
21	assumption		⊢
22	instantiation	45	⊢
	: , :
23	axiom		⊢
	proveit.logic.equality.equals_reflexivity
24	theorem		⊢
	proveit.logic.equality.equals_reversal
25	instantiation	31, 32	, , , ,  ⊢
	: , : , :
26	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
27	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
28	instantiation	33	⊢
	: , : , : , :
29	instantiation	33	⊢
	: , : , : , :
30	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_association
31	axiom		⊢
	proveit.logic.equality.substitution
32	instantiation	34, 35, 64, 36, 37, 38, 39, 40, 41, 42	, , , ,  ⊢
	: , : , : , : , : , : , : , : , : , :
33	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
34	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_disassociation
35	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
36	instantiation	45	⊢
	: , :
37	instantiation	43, 44	⊢
	:
38	instantiation	45	⊢
	: , :
39	assumption		⊢
40	assumption		⊢
41	instantiation	46, 47	,  ⊢
	:
42	assumption		⊢
43	theorem		⊢
	proveit.linear_algebra.real_vec_set_is_vec_space
44	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
45	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
46	assumption		⊢
47	instantiation	48, 49, 50	⊢
	:
48	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
49	instantiation	65, 51, 63	⊢
	: , : , :
50	instantiation	52, 53	⊢
	: , :
51	instantiation	54, 61, 62	⊢
	: , :
52	theorem		⊢
	proveit.numbers.ordering.relax_less
53	instantiation	55, 56, 57	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
55	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
56	instantiation	58, 59	⊢
	:
57	instantiation	60, 61, 62, 63	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
59	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
60	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
61	instantiation	65, 66, 64	⊢
	: , : , :
62	instantiation	65, 66, 67	⊢
	: , : , :
63	assumption		⊢
64	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
65	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
66	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
67	theorem		⊢
	proveit.numbers.numerals.decimals.nat4