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	modus ponens	1, 2	⊢
1	instantiation	3, 9, 14, 4	⊢
	: , : , : , : , : , : , : , :
2	modus ponens	5, 6	⊢
3	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.distribution_over_vec_sum_with_scalar_mult
4	instantiation	21, 22, 7	⊢
	: , :
5	instantiation	8, 9, 14	⊢
	: , : , : , : , : , :
6	generalization	10	⊢
7	instantiation	49, 11, 12	⊢
	: , : , :
8	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
9	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
10	instantiation	13, 14, 15, 16	,  ⊢
	: , : , : , :
11	instantiation	66, 52, 17	⊢
	: , :
12	instantiation	44, 18, 19	⊢
	: , : , :
13	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
14	instantiation	20, 37, 25, 26, 27	⊢
	: , : , :
15	instantiation	21, 22, 23	,  ⊢
	: , :
16	instantiation	24, 37, 25, 26, 27, 28, 29, 30	,  ⊢
	: , : , : , :
17	instantiation	49, 31, 32	⊢
	: , : , :
18	instantiation	58, 100, 53, 59, 33, 60, 52, 67, 68, 41	⊢
	: , : , : , : , : , :
19	instantiation	58, 59, 95, 53, 60, 54, 33, 63, 64, 67, 68, 41	⊢
	: , : , : , : , : , :
20	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
21	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
22	instantiation	98, 73, 34	⊢
	: , : , :
23	instantiation	49, 35, 36	,  ⊢
	: , : , :
24	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
25	instantiation	69	⊢
	: , :
26	instantiation	38, 37	⊢
	:
27	instantiation	38, 39	⊢
	:
28	instantiation	69	⊢
	: , :
29	theorem		⊢
	proveit.physics.quantum.algebra.ket_one_in_qubit_space
30	instantiation	40, 97, 83	,  ⊢
	: , :
31	instantiation	66, 57, 41	⊢
	: , :
32	instantiation	58, 59, 95, 100, 60, 61, 67, 68, 41	⊢
	: , : , : , : , : , :
33	instantiation	65	⊢
	: , : , :
34	instantiation	98, 78, 42	⊢
	: , : , :
35	instantiation	66, 52, 43	,  ⊢
	: , :
36	instantiation	44, 45, 46	,  ⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
38	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
39	instantiation	47, 95, 92	⊢
	: , :
40	theorem		⊢
	proveit.physics.quantum.algebra.num_ket_in_register_space
41	instantiation	98, 73, 48	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
43	instantiation	49, 50, 51	,  ⊢
	: , : , :
44	axiom		⊢
	proveit.logic.equality.equals_transitivity
45	instantiation	58, 100, 53, 59, 55, 60, 52, 67, 68, 62	,  ⊢
	: , : , : , : , : , :
46	instantiation	58, 59, 95, 53, 60, 54, 55, 63, 64, 67, 68, 62	,  ⊢
	: , : , : , : , : , :
47	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
48	instantiation	98, 76, 56	⊢
	: , : , :
49	theorem		⊢
	proveit.logic.equality.sub_right_side_into
50	instantiation	66, 57, 62	,  ⊢
	: , :
51	instantiation	58, 59, 95, 100, 60, 61, 67, 68, 62	,  ⊢
	: , : , : , : , : , :
52	instantiation	66, 63, 64	⊢
	: , :
53	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
54	instantiation	69	⊢
	: , :
55	instantiation	65	⊢
	: , : , :
56	instantiation	98, 81, 88	⊢
	: , : , :
57	instantiation	66, 67, 68	⊢
	: , :
58	theorem		⊢
	proveit.numbers.multiplication.disassociation
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	69	⊢
	: , :
62	instantiation	98, 73, 70	,  ⊢
	: , : , :
63	instantiation	98, 73, 71	⊢
	: , : , :
64	instantiation	98, 73, 72	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
66	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
67	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
68	instantiation	98, 73, 74	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
70	instantiation	98, 76, 75	,  ⊢
	: , : , :
71	instantiation	98, 76, 77	⊢
	: , : , :
72	instantiation	98, 78, 79	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
74	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
75	instantiation	98, 81, 80	,  ⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
77	instantiation	98, 81, 91	⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
79	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
80	instantiation	98, 82, 83	,  ⊢
	: , : , :
81	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
82	instantiation	84, 85, 86	⊢
	: , :
83	assumption		⊢
84	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
85	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
86	instantiation	87, 88, 89	⊢
	: , :
87	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
88	instantiation	90, 91, 92	⊢
	: , :
89	instantiation	93, 94	⊢
	:
90	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
91	instantiation	98, 99, 95	⊢
	: , : , :
92	instantiation	98, 96, 97	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.negation.int_closure
94	instantiation	98, 99, 100	⊢
	: , : , :
95	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
96	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
97	assumption		⊢
98	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
99	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
100	theorem		⊢
	proveit.numbers.numerals.decimals.nat1