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	8	⊢
2	instantiation	17, 4	, ,  ⊢
	: , : , :
3	instantiation	5, 26, 32, 41, 35, 13, 6, 15, 7*	, , , ,  ⊢
	: , : , : , : , : , : , : , : , : , :
4	instantiation	8, 9, 10	, ,  ⊢
	: , : , :
5	theorem		⊢
	proveit.linear_algebra.tensors.factor_scalar_from_tensor_prod
6	instantiation	39, 61, 40, 41, 12, 43, 14	,  ⊢
	: , : , : , :
7	instantiation	11, 32, 66, 40, 41, 12, 13, 43, 14, 15	, , ,  ⊢
	: , : , : , : , : , : , : , : , : , :
8	axiom		⊢
	proveit.logic.equality.equals_transitivity
9	instantiation	23, 16	, ,  ⊢
	: , :
10	instantiation	17, 18	,  ⊢
	: , : , :
11	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_disassociation
12	instantiation	47	⊢
	: , :
13	assumption		⊢
14	modus ponens	19, 20	⊢
15	assumption		⊢
16	modus ponens	21, 22	, ,  ⊢
17	axiom		⊢
	proveit.logic.equality.substitution
18	instantiation	23, 24	,  ⊢
	: , :
19	instantiation	30, 33, 41	⊢
	: , : , : , : , : , :
20	generalization	44	⊢
21	instantiation	25, 33, 35, 26	⊢
	: , : , : , : , : , : , :
22	modus ponens	27, 29	,  ⊢
23	theorem		⊢
	proveit.logic.equality.equals_reversal
24	modus ponens	28, 29	,  ⊢
25	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.distribution_over_vec_sum
26	assumption		⊢
27	instantiation	30, 33, 35	⊢
	: , : , : , : , : , :
28	instantiation	31, 32, 33, 34, 35, 36	⊢
	: , : , : , : , : , : , : , : , : , :
29	generalization	37	,  ⊢
30	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
31	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_distribution_over_summation
32	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
33	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
34	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
35	instantiation	38, 61, 40, 41	⊢
	: , : , :
36	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
37	instantiation	39, 61, 40, 41, 42, 43, 44	, ,  ⊢
	: , : , : , :
38	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
39	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
40	instantiation	47	⊢
	: , :
41	instantiation	45, 46	⊢
	:
42	instantiation	47	⊢
	: , :
43	assumption		⊢
44	instantiation	48, 49	,  ⊢
	:
45	theorem		⊢
	proveit.linear_algebra.real_vec_set_is_vec_space
46	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
47	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
48	assumption		⊢
49	instantiation	50, 51, 52	⊢
	:
50	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
51	instantiation	67, 53, 65	⊢
	: , : , :
52	instantiation	54, 55	⊢
	: , :
53	instantiation	56, 63, 64	⊢
	: , :
54	theorem		⊢
	proveit.numbers.ordering.relax_less
55	instantiation	57, 58, 59	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
57	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
58	instantiation	60, 61	⊢
	:
59	instantiation	62, 63, 64, 65	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
61	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
62	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
63	instantiation	67, 68, 66	⊢
	: , : , :
64	instantiation	67, 68, 69	⊢
	: , : , :
65	assumption		⊢
66	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
67	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
68	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
69	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
*equality replacement requirements