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, 4*	, , , ,  ⊢
	: , : , :
1	reference	22	⊢
2	instantiation	32, 5, 6*, 7*	, , ,  ⊢
	: , : , :
3	instantiation	42, 8	, , , ,  ⊢
	: , :
4	instantiation	22, 9, 10	, , , ,  ⊢
	: , : , :
5	modus ponens	11, 12	, , ,  ⊢
6	instantiation	13, 94	⊢
	: , :
7	instantiation	13, 94	⊢
	: , :
8	modus ponens	14, 15	, , , ,  ⊢
9	instantiation	32, 16	, ,  ⊢
	: , : , :
10	instantiation	39, 48, 60, 70, 63, 56, 17, 57, 18*	, , , ,  ⊢
	: , : , : , : , : , : , : , : , : , :
11	instantiation	19, 61	⊢
	: , : , : , : , : , : , :
12	generalization	46	, , ,  ⊢
13	theorem		⊢
	proveit.core_expr_types.conditionals.satisfied_condition_reduction
14	instantiation	20, 60, 61, 37	⊢
	: , : , : , : , : , : , : , : , : , : , :
15	generalization	21	, , , ,  ⊢
16	instantiation	22, 23, 24	, ,  ⊢
	: , : , :
17	instantiation	68, 90, 69, 70, 26, 72, 27	,  ⊢
	: , : , : , :
18	instantiation	25, 60, 95, 69, 70, 26, 56, 72, 27, 57	, , ,  ⊢
	: , : , : , : , : , : , : , : , : , :
19	theorem		⊢
	proveit.core_expr_types.lambda_maps.general_lambda_substitution
20	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_distribution_over_summation_with_scalar_mult
21	instantiation	28, 29, 30	, , , , ,  ⊢
	: , : , :
22	axiom		⊢
	proveit.logic.equality.equals_transitivity
23	instantiation	42, 31	, ,  ⊢
	: , :
24	instantiation	32, 33	,  ⊢
	: , : , :
25	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_disassociation
26	instantiation	76	⊢
	: , :
27	modus ponens	34, 35	⊢
28	theorem		⊢
	proveit.logic.equality.sub_left_side_into
29	instantiation	36, 37, 48, 38	, , , , ,  ⊢
	: , : , : , :
30	instantiation	39, 48, 60, 70, 63, 56, 65, 57	, , , , ,  ⊢
	: , : , : , : , : , : , : , : , : , :
31	modus ponens	40, 41	, ,  ⊢
32	axiom		⊢
	proveit.logic.equality.substitution
33	instantiation	42, 43	,  ⊢
	: , :
34	instantiation	58, 61, 70	⊢
	: , : , : , : , : , :
35	generalization	73	⊢
36	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
37	instantiation	67, 52, 53, 70	⊢
	: , : , :
38	instantiation	44, 45, 46	, , , ,  ⊢
	: , : , :
39	theorem		⊢
	proveit.linear_algebra.tensors.factor_scalar_from_tensor_prod
40	instantiation	47, 61, 63, 48	⊢
	: , : , : , : , : , : , :
41	modus ponens	49, 51	,  ⊢
42	theorem		⊢
	proveit.logic.equality.equals_reversal
43	modus ponens	50, 51	,  ⊢
44	theorem		⊢
	proveit.logic.equality.sub_right_side_into
45	instantiation	68, 52, 53, 70, 54, 56, 72, 73, 57	, , , ,  ⊢
	: , : , : , :
46	instantiation	55, 60, 95, 69, 70, 71, 56, 72, 73, 57	, , , ,  ⊢
	: , : , : , : , : , : , : , : , : , :
47	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.distribution_over_vec_sum
48	assumption		⊢
49	instantiation	58, 61, 63	⊢
	: , : , : , : , : , :
50	instantiation	59, 60, 61, 62, 63, 64	⊢
	: , : , : , : , : , : , : , : , : , :
51	generalization	65	,  ⊢
52	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
53	instantiation	66	⊢
	: , : , : , :
54	instantiation	66	⊢
	: , : , : , :
55	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_association
56	assumption		⊢
57	assumption		⊢
58	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
59	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_distribution_over_summation
60	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
61	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
62	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
63	instantiation	67, 90, 69, 70	⊢
	: , : , :
64	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
65	instantiation	68, 90, 69, 70, 71, 72, 73	, ,  ⊢
	: , : , : , :
66	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
67	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
68	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
69	instantiation	76	⊢
	: , :
70	instantiation	74, 75	⊢
	:
71	instantiation	76	⊢
	: , :
72	assumption		⊢
73	instantiation	77, 78	,  ⊢
	:
74	theorem		⊢
	proveit.linear_algebra.real_vec_set_is_vec_space
75	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
76	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
77	assumption		⊢
78	instantiation	79, 80, 81	⊢
	:
79	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
80	instantiation	96, 82, 94	⊢
	: , : , :
81	instantiation	83, 84	⊢
	: , :
82	instantiation	85, 92, 93	⊢
	: , :
83	theorem		⊢
	proveit.numbers.ordering.relax_less
84	instantiation	86, 87, 88	⊢
	: , : , :
85	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
86	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
87	instantiation	89, 90	⊢
	:
88	instantiation	91, 92, 93, 94	⊢
	: , : , :
89	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
90	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
91	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
92	instantiation	96, 97, 95	⊢
	: , : , :
93	instantiation	96, 97, 98	⊢
	: , : , :
94	assumption		⊢
95	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
96	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
97	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
98	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
*equality replacement requirements