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	55	⊢
2	instantiation	87, 5, 6*, 7*	, , , ,  ⊢
	: , : , :
3	instantiation	59, 8	, , , ,  ⊢
	: , :
4	instantiation	55, 9, 10	, , , ,  ⊢
	: , : , :
5	modus ponens	11, 12	, , , ,  ⊢
6	instantiation	13, 110	⊢
	: , :
7	instantiation	13, 110	⊢
	: , :
8	modus ponens	14, 15	, , , ,  ⊢
9	instantiation	87, 16	, ,  ⊢
	: , : , :
10	instantiation	69, 70, 71, 78, 72, 46, 73	, , , ,  ⊢
	: , : , : , : , : , : , : , : , : , :
11	instantiation	17, 77	⊢
	: , : , : , : , : , : , :
12	generalization	18	, , , ,  ⊢
13	theorem		⊢
	proveit.core_expr_types.conditionals.satisfied_condition_reduction
14	instantiation	19, 71, 77, 36	⊢
	: , : , : , : , : , : , : , : , : , : , :
15	generalization	20	, , , ,  ⊢
16	instantiation	55, 21, 22	, ,  ⊢
	: , : , :
17	theorem		⊢
	proveit.core_expr_types.lambda_maps.general_lambda_substitution
18	instantiation	23, 24, 25, 93, 94	, , , , ,  ⊢
	: , : , : , : , :
19	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_distribution_over_summation_with_scalar_mult
20	instantiation	51, 26, 27	, , , , ,  ⊢
	: , : , :
21	instantiation	87, 28	,  ⊢
	: , : , :
22	instantiation	59, 29	, ,  ⊢
	: , :
23	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.doubly_scaled_as_singly_scaled
24	instantiation	50, 84, 30, 31	⊢
	: , : , :
25	instantiation	52, 84, 30, 31, 54, 32, 33, 34	, , ,  ⊢
	: , : , : , :
26	instantiation	35, 36, 37, 38	, , , , ,  ⊢
	: , : , : , :
27	instantiation	39, 40, 41, 42	, , , , ,  ⊢
	: , : , : , :
28	modus ponens	43, 44	,  ⊢
29	modus ponens	45, 46	, ,  ⊢
30	instantiation	68	⊢
	: , : , :
31	instantiation	47, 84	⊢
	:
32	instantiation	48, 49, 72	⊢
	: , : , :
33	instantiation	48, 49, 79	,  ⊢
	: , : , :
34	instantiation	48, 49, 73	⊢
	: , : , :
35	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
36	instantiation	50, 84, 53, 78	⊢
	: , : , :
37	instantiation	51, 70, 88	,  ⊢
	: , : , :
38	instantiation	52, 84, 53, 78, 54, 72, 79, 73	, , ,  ⊢
	: , : , : , :
39	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
40	instantiation	55, 56, 57	, , , , ,  ⊢
	: , : , :
41	instantiation	58	⊢
	:
42	instantiation	59, 60	,  ⊢
	: , :
43	instantiation	61, 77	⊢
	: , : , : , : , : , :
44	generalization	62	,  ⊢
45	instantiation	63, 77, 78, 70	,  ⊢
	: , : , : , : , : , : , :
46	modus ponens	64, 65	⊢
47	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
48	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
49	instantiation	66, 84, 67	⊢
	: , : , :
50	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
51	theorem		⊢
	proveit.logic.equality.sub_left_side_into
52	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
53	instantiation	68	⊢
	: , : , :
54	instantiation	68	⊢
	: , : , :
55	axiom		⊢
	proveit.logic.equality.equals_transitivity
56	instantiation	87, 82	,  ⊢
	: , : , :
57	instantiation	69, 70, 71, 78, 72, 79, 73	, , , , ,  ⊢
	: , : , : , : , : , : , : , : , : , :
58	axiom		⊢
	proveit.logic.equality.equals_reflexivity
59	theorem		⊢
	proveit.logic.equality.equals_reversal
60	instantiation	87, 88	,  ⊢
	: , : , :
61	axiom		⊢
	proveit.core_expr_types.lambda_maps.lambda_substitution
62	instantiation	74, 75	,  ⊢
	: , : , :
63	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.distribution_over_vec_sum
64	instantiation	76, 77, 78	⊢
	: , : , : , : , : , :
65	generalization	79	⊢
66	theorem		⊢
	proveit.logic.sets.cartesian_products.cart_exp_subset_eq
67	instantiation	80, 99	⊢
	: , :
68	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
69	theorem		⊢
	proveit.linear_algebra.tensors.factor_scalar_from_tensor_prod
70	instantiation	81, 98, 100	,  ⊢
	: , :
71	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
72	assumption		⊢
73	assumption		⊢
74	axiom		⊢
	proveit.core_expr_types.conditionals.conditional_substitution
75	deduction	82	,  ⊢
76	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
77	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
78	instantiation	83, 84	⊢
	:
79	instantiation	85, 86	,  ⊢
	:
80	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
81	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
82	instantiation	87, 88	,  ⊢
	: , : , :
83	theorem		⊢
	proveit.linear_algebra.real_vec_set_is_vec_space
84	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
85	assumption		⊢
86	instantiation	89, 90, 91	⊢
	:
87	axiom		⊢
	proveit.logic.equality.substitution
88	instantiation	92, 93, 94	,  ⊢
	: , :
89	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
90	instantiation	112, 95, 110	⊢
	: , : , :
91	instantiation	96, 97	⊢
	: , :
92	axiom		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult
93	instantiation	112, 99, 98	⊢
	: , : , :
94	instantiation	112, 99, 100	⊢
	: , : , :
95	instantiation	101, 108, 109	⊢
	: , :
96	theorem		⊢
	proveit.numbers.ordering.relax_less
97	instantiation	102, 103, 104	⊢
	: , : , :
98	assumption		⊢
99	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
100	assumption		⊢
101	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
102	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
103	instantiation	105, 106	⊢
	:
104	instantiation	107, 108, 109, 110	⊢
	: , : , :
105	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
106	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
107	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
108	instantiation	112, 113, 111	⊢
	: , : , :
109	instantiation	112, 113, 114	⊢
	: , : , :
110	assumption		⊢
111	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
112	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
113	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
114	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
*equality replacement requirements