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, 5, 6, 7*	, ,  ⊢
	: , : , : , : , :
1	theorem		⊢
	proveit.linear_algebra.addition.vec_sum_of_constant_vec
2	reference	87	⊢
3	reference	89	⊢
4	instantiation	8, 55, 9, 10, 11*, 47*	⊢
	: , : , :
5	instantiation	12, 76, 13, 61	⊢
	: , : , :
6	instantiation	75, 76, 13, 61, 14, 15, 33	, ,  ⊢
	: , : , : , :
7	instantiation	39, 16, 17	, ,  ⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
9	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
10	instantiation	18, 98	⊢
	:
11	instantiation	19, 20, 21	⊢
	: , : , :
12	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
13	instantiation	91	⊢
	: , :
14	instantiation	91	⊢
	: , :
15	instantiation	38, 61, 105, 92	,  ⊢
	: , : , : , :
16	instantiation	22, 98, 23, 24, 25, 26	, ,  ⊢
	: , : , : , :
17	instantiation	50, 51, 52, 35, 36, 27*	, ,  ⊢
	: , : , : , : , :
18	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
19	theorem		⊢
	proveit.logic.equality.sub_right_side_into
20	instantiation	28, 45	⊢
	:
21	instantiation	29, 45, 30	⊢
	: , :
22	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
23	instantiation	91	⊢
	: , :
24	instantiation	91	⊢
	: , :
25	instantiation	39, 31, 32	⊢
	: , : , :
26	instantiation	57, 105, 59, 58, 60, 61, 92, 33, 34*	, ,  ⊢
	: , : , : , : , : , : , : , : , : , :
27	instantiation	65, 35, 36	⊢
	: , :
28	theorem		⊢
	proveit.numbers.addition.elim_zero_right
29	theorem		⊢
	proveit.numbers.addition.commutation
30	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
31	instantiation	48, 37	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_1
33	instantiation	38, 61, 105, 95	,  ⊢
	: , : , : , :
34	instantiation	39, 40, 41	, ,  ⊢
	: , : , :
35	instantiation	104, 107, 42	⊢
	: , : , :
36	instantiation	43, 97, 45	⊢
	: , :
37	instantiation	44, 45, 46, 47	⊢
	: , : , :
38	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
39	axiom		⊢
	proveit.logic.equality.equals_transitivity
40	instantiation	48, 49	, ,  ⊢
	: , : , :
41	instantiation	50, 51, 52, 97, 53*	, ,  ⊢
	: , : , : , : , :
42	instantiation	104, 69, 54	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
44	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
45	instantiation	104, 107, 55	⊢
	: , : , :
46	instantiation	104, 107, 56	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
48	axiom		⊢
	proveit.logic.equality.substitution
49	instantiation	57, 105, 58, 59, 60, 61, 92, 95	, ,  ⊢
	: , : , : , : , : , : , : , : , : , :
50	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.doubly_scaled_as_singly_scaled
51	instantiation	90, 62	⊢
	:
52	instantiation	93, 63, 64	,  ⊢
	: , : , :
53	instantiation	65, 97, 66*	⊢
	: , :
54	instantiation	104, 88, 67	⊢
	: , : , :
55	instantiation	104, 69, 68	⊢
	: , : , :
56	instantiation	104, 69, 70	⊢
	: , : , :
57	theorem		⊢
	proveit.linear_algebra.tensors.factor_scalar_from_tensor_prod
58	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
59	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
60	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
61	instantiation	71, 102	⊢
	:
62	theorem		⊢
	proveit.numbers.numerals.decimals.posnat9
63	instantiation	72, 76, 73, 102, 74*	⊢
	: , : , :
64	instantiation	75, 76, 77, 78, 79, 80, 81	,  ⊢
	: , : , : , :
65	axiom		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult
66	instantiation	82, 97, 83, 84*, 85*	⊢
	: , : , :
67	instantiation	104, 99, 86	⊢
	: , : , :
68	instantiation	104, 88, 87	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
70	instantiation	104, 88, 89	⊢
	: , : , :
71	theorem		⊢
	proveit.linear_algebra.real_vec_set_is_vec_space
72	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_cart_exps_within_cart_exp
73	instantiation	91	⊢
	: , :
74	theorem		⊢
	proveit.numbers.numerals.decimals.mult_3_3
75	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
76	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
77	instantiation	91	⊢
	: , :
78	instantiation	90, 102	⊢
	:
79	instantiation	91	⊢
	: , :
80	instantiation	93, 94, 92	⊢
	: , : , :
81	instantiation	93, 94, 95	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.exponentiation.product_of_posnat_powers
83	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
84	instantiation	96, 97	⊢
	:
85	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
86	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
87	instantiation	104, 99, 98	⊢
	: , : , :
88	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
89	instantiation	104, 99, 100	⊢
	: , : , :
90	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
91	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
92	assumption		⊢
93	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
94	instantiation	101, 102, 103	⊢
	: , : , :
95	assumption		⊢
96	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
97	instantiation	104, 107, 105	⊢
	: , : , :
98	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
99	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
100	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
101	theorem		⊢
	proveit.logic.sets.cartesian_products.cart_exp_subset_eq
102	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
103	instantiation	106, 107	⊢
	: , :
104	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
105	assumption		⊢
106	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
107	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
*equality replacement requirements