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	reference	32	⊢
2	modus ponens	4, 5	, , , ,  ⊢
3	instantiation	6, 7, 8	, , , ,  ⊢
	: , : , :
4	instantiation	9, 78, 46, 49, 17, 30	⊢
	: , : , : , : , : , : , : , : , : , : , :
5	generalization	10	, , , ,  ⊢
6	axiom		⊢
	proveit.logic.equality.equals_transitivity
7	instantiation	43, 11	,  ⊢
	: , : , :
8	instantiation	29, 35, 78, 49, 50, 51, 30, 53, 54, 24, 56	, , , ,  ⊢
	: , : , : , : , : , : , : , : , : , :
9	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_distribution_over_summation_with_scalar_mult
10	instantiation	12, 13, 14	, , , , ,  ⊢
	: , : , :
11	instantiation	32, 15	,  ⊢
	: , :
12	theorem		⊢
	proveit.logic.equality.sub_left_side_into
13	instantiation	16, 17, 35, 18	, , , , ,  ⊢
	: , : , : , :
14	instantiation	19, 20, 21, 22	, , , , ,  ⊢
	: , : , : , :
15	modus ponens	23, 24	,  ⊢
16	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
17	instantiation	25, 39, 40, 51	⊢
	: , : , :
18	instantiation	26, 27, 28	, , , ,  ⊢
	: , : , :
19	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
20	instantiation	29, 35, 78, 49, 50, 51, 30, 53, 54, 55, 56	, , , , ,  ⊢
	: , : , : , : , : , : , : , : , : , :
21	instantiation	31	⊢
	:
22	instantiation	32, 33	, , , ,  ⊢
	: , :
23	instantiation	34, 46, 51, 35	⊢
	: , : , : , : , : , : , :
24	modus ponens	36, 37	⊢
25	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
26	theorem		⊢
	proveit.logic.equality.sub_right_side_into
27	instantiation	38, 39, 40, 51, 41, 53, 54, 55, 56	, , , ,  ⊢
	: , : , : , :
28	instantiation	42, 49, 78, 50, 51, 52, 53, 54, 55, 56	, , , ,  ⊢
	: , : , : , : , : , : , : , : , : , :
29	theorem		⊢
	proveit.linear_algebra.tensors.factor_scalar_from_tensor_prod
30	instantiation	59	⊢
	: , :
31	axiom		⊢
	proveit.logic.equality.equals_reflexivity
32	theorem		⊢
	proveit.logic.equality.equals_reversal
33	instantiation	43, 44	, , , ,  ⊢
	: , : , :
34	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.distribution_over_vec_sum
35	assumption		⊢
36	instantiation	45, 46, 51	⊢
	: , : , : , : , : , :
37	generalization	55	⊢
38	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
39	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
40	instantiation	47	⊢
	: , : , : , :
41	instantiation	47	⊢
	: , : , : , :
42	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_association
43	axiom		⊢
	proveit.logic.equality.substitution
44	instantiation	48, 49, 78, 50, 51, 52, 53, 54, 55, 56	, , , ,  ⊢
	: , : , : , : , : , : , : , : , : , :
45	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
46	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
47	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
48	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_disassociation
49	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
50	instantiation	59	⊢
	: , :
51	instantiation	57, 58	⊢
	:
52	instantiation	59	⊢
	: , :
53	assumption		⊢
54	assumption		⊢
55	instantiation	60, 61	,  ⊢
	:
56	assumption		⊢
57	theorem		⊢
	proveit.linear_algebra.real_vec_set_is_vec_space
58	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
59	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
60	assumption		⊢
61	instantiation	62, 63, 64	⊢
	:
62	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
63	instantiation	79, 65, 77	⊢
	: , : , :
64	instantiation	66, 67	⊢
	: , :
65	instantiation	68, 75, 76	⊢
	: , :
66	theorem		⊢
	proveit.numbers.ordering.relax_less
67	instantiation	69, 70, 71	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
69	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
70	instantiation	72, 73	⊢
	:
71	instantiation	74, 75, 76, 77	⊢
	: , : , :
72	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
73	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
74	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
75	instantiation	79, 80, 78	⊢
	: , : , :
76	instantiation	79, 80, 81	⊢
	: , : , :
77	assumption		⊢
78	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
79	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
80	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
81	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
*equality replacement requirements