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	63	⊢
2	instantiation	4, 5	⊢
	: , : , :
3	modus ponens	6, 7	⊢
4	axiom		⊢
	proveit.logic.equality.substitution
5	instantiation	8, 9	⊢
	: , :
6	instantiation	10, 77, 114, 119, 11, 78, 12	⊢
	: , : , : , : , : , : , : , :
7	instantiation	13, 14, 15	⊢
	: , : , :
8	theorem		⊢
	proveit.logic.equality.equals_reversal
9	instantiation	16, 32, 77, 119, 78, 31, 40, 33, 24	⊢
	: , : , : , : , : , : , : , : , : , :
10	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_factorization_from_add
11	instantiation	45, 17	⊢
	:
12	instantiation	88	⊢
	: , :
13	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
14	instantiation	18, 37, 19, 46	⊢
	: , : , :
15	instantiation	20, 37, 21, 31, 40, 22, 23, 24	⊢
	: , : , : , :
16	theorem		⊢
	proveit.linear_algebra.tensors.factor_scalar_from_tensor_prod
17	instantiation	25, 37, 46	⊢
	: , :
18	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_cart_exps_within_cart_exp
19	instantiation	88	⊢
	: , :
20	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
21	instantiation	88	⊢
	: , :
22	instantiation	88	⊢
	: , :
23	instantiation	26, 31, 27, 28	⊢
	: , : , : , :
24	modus ponens	29, 30	⊢
25	theorem		⊢
	proveit.numbers.multiplication.mult_nat_pos_closure_bin
26	theorem		⊢
	proveit.linear_algebra.addition.binary_closure
27	theorem		⊢
	proveit.physics.quantum.algebra.ket_zero_in_qubit_space
28	instantiation	39, 31, 32, 33	⊢
	: , : , : , :
29	instantiation	34, 35, 40	⊢
	: , : , : , : , : , :
30	generalization	36	⊢
31	instantiation	45, 37	⊢
	:
32	instantiation	47, 48, 38	⊢
	: , :
33	theorem		⊢
	proveit.physics.quantum.algebra.ket_one_in_qubit_space
34	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
35	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
36	instantiation	39, 40, 41, 42	,  ⊢
	: , : , : , :
37	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
38	instantiation	67, 43, 44	⊢
	: , : , :
39	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
40	instantiation	45, 46	⊢
	:
41	instantiation	47, 48, 49	,  ⊢
	: , :
42	instantiation	50, 116, 102	,  ⊢
	: , :
43	instantiation	85, 70, 51	⊢
	: , :
44	instantiation	63, 52, 53	⊢
	: , : , :
45	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
46	instantiation	54, 114, 111	⊢
	: , :
47	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
48	instantiation	117, 92, 55	⊢
	: , : , :
49	instantiation	67, 56, 57	,  ⊢
	: , : , :
50	theorem		⊢
	proveit.physics.quantum.algebra.num_ket_in_register_space
51	instantiation	67, 58, 59	⊢
	: , : , :
52	instantiation	76, 119, 71, 77, 60, 78, 70, 86, 87, 66	⊢
	: , : , : , : , : , :
53	instantiation	76, 77, 114, 71, 78, 72, 60, 81, 82, 86, 87, 66	⊢
	: , : , : , : , : , :
54	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
55	instantiation	117, 97, 61	⊢
	: , : , :
56	instantiation	85, 70, 62	,  ⊢
	: , :
57	instantiation	63, 64, 65	,  ⊢
	: , : , :
58	instantiation	85, 75, 66	⊢
	: , :
59	instantiation	76, 77, 114, 119, 78, 79, 86, 87, 66	⊢
	: , : , : , : , : , :
60	instantiation	83	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
62	instantiation	67, 68, 69	,  ⊢
	: , : , :
63	axiom		⊢
	proveit.logic.equality.equals_transitivity
64	instantiation	76, 119, 71, 77, 73, 78, 70, 86, 87, 80	,  ⊢
	: , : , : , : , : , :
65	instantiation	76, 77, 114, 71, 78, 72, 73, 81, 82, 86, 87, 80	,  ⊢
	: , : , : , : , : , :
66	instantiation	117, 92, 74	⊢
	: , : , :
67	theorem		⊢
	proveit.logic.equality.sub_right_side_into
68	instantiation	85, 75, 80	,  ⊢
	: , :
69	instantiation	76, 77, 114, 119, 78, 79, 86, 87, 80	,  ⊢
	: , : , : , : , : , :
70	instantiation	85, 81, 82	⊢
	: , :
71	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
72	instantiation	88	⊢
	: , :
73	instantiation	83	⊢
	: , : , :
74	instantiation	117, 95, 84	⊢
	: , : , :
75	instantiation	85, 86, 87	⊢
	: , :
76	theorem		⊢
	proveit.numbers.multiplication.disassociation
77	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
78	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
79	instantiation	88	⊢
	: , :
80	instantiation	117, 92, 89	,  ⊢
	: , : , :
81	instantiation	117, 92, 90	⊢
	: , : , :
82	instantiation	117, 92, 91	⊢
	: , : , :
83	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
84	instantiation	117, 100, 107	⊢
	: , : , :
85	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
86	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
87	instantiation	117, 92, 93	⊢
	: , : , :
88	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
89	instantiation	117, 95, 94	,  ⊢
	: , : , :
90	instantiation	117, 95, 96	⊢
	: , : , :
91	instantiation	117, 97, 98	⊢
	: , : , :
92	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
93	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
94	instantiation	117, 100, 99	,  ⊢
	: , : , :
95	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
96	instantiation	117, 100, 110	⊢
	: , : , :
97	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
98	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
99	instantiation	117, 101, 102	,  ⊢
	: , : , :
100	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
101	instantiation	103, 104, 105	⊢
	: , :
102	assumption		⊢
103	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
104	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
105	instantiation	106, 107, 108	⊢
	: , :
106	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
107	instantiation	109, 110, 111	⊢
	: , :
108	instantiation	112, 113	⊢
	:
109	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
110	instantiation	117, 118, 114	⊢
	: , : , :
111	instantiation	117, 115, 116	⊢
	: , : , :
112	theorem		⊢
	proveit.numbers.negation.int_closure
113	instantiation	117, 118, 119	⊢
	: , : , :
114	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
115	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
116	assumption		⊢
117	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
118	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
119	theorem		⊢
	proveit.numbers.numerals.decimals.nat1