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	theorem		⊢
	proveit.logic.equality.sub_left_side_into
2	instantiation	4, 84, 5, 6*	⊢
	:
3	instantiation	115, 7	⊢
	: , : , :
4	axiom		⊢
	proveit.physics.quantum.QPE._psi_t_def
5	instantiation	77, 8, 9	⊢
	: , : , :
6	instantiation	106, 10, 11	⊢
	: , : , :
7	instantiation	12, 13, 125, 14, 15*, 16*	⊢
	: , : , : , :
8	instantiation	17, 18, 105, 91	⊢
	: , : , :
9	instantiation	19, 105, 20	⊢
	: , :
10	instantiation	115, 21	⊢
	: , : , :
11	instantiation	22, 54, 23	⊢
	: , : , :
12	theorem		⊢
	proveit.linear_algebra.addition.vec_sum_split_first
13	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
14	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
15	instantiation	106, 24, 25	⊢
	: , : , :
16	instantiation	106, 26, 27	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
18	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
19	theorem		⊢
	proveit.numbers.addition.commutation
20	instantiation	28, 105	⊢
	:
21	instantiation	29, 84, 30	⊢
	: , : , :
22	axiom		⊢
	proveit.linear_algebra.tensors.unary_tensor_prod_def
23	instantiation	53, 54, 31, 32	⊢
	: , : , : , :
24	instantiation	115, 33	⊢
	: , : , :
25	instantiation	34, 105, 43, 54	⊢
	: , : , :
26	instantiation	115, 35	⊢
	: , : , :
27	instantiation	36, 125, 37*	⊢
	: , :
28	theorem		⊢
	proveit.numbers.negation.complex_closure
29	theorem		⊢
	proveit.core_expr_types.tuples.tuple_eq_via_elem_eq
30	instantiation	115, 38	⊢
	: , : , :
31	instantiation	39, 105, 40, 41	⊢
	: , :
32	instantiation	42, 54, 43, 44	⊢
	: , : , : , :
33	instantiation	106, 45, 46	⊢
	: , : , :
34	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.one_as_scalar_mult_id
35	modus ponens	47, 48	⊢
36	axiom		⊢
	proveit.linear_algebra.addition.vec_sum_single
37	instantiation	93, 69, 98, 70, 99, 118, 111, 102, 103	⊢
	: , : , : , :
38	instantiation	115, 49	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.division.div_complex_closure
40	instantiation	50, 118	⊢
	:
41	instantiation	51, 63, 52	⊢
	: , :
42	theorem		⊢
	proveit.linear_algebra.addition.binary_closure
43	theorem		⊢
	proveit.physics.quantum.algebra.ket_zero_in_qubit_space
44	instantiation	53, 54, 55, 56	⊢
	: , : , : , :
45	instantiation	115, 57	⊢
	: , : , :
46	instantiation	117, 66	⊢
	:
47	instantiation	58, 84	⊢
	: , : , : , : , : , :
48	generalization	59	⊢
49	instantiation	115, 60	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.exponentiation.sqrt_complex_closure
51	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
52	instantiation	61, 62, 63	⊢
	: , :
53	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
54	instantiation	64, 86	⊢
	:
55	instantiation	65, 66, 67	⊢
	: , :
56	theorem		⊢
	proveit.physics.quantum.algebra.ket_one_in_qubit_space
57	instantiation	68, 69, 98, 70, 99, 118, 111, 102, 103	⊢
	: , : , : , :
58	axiom		⊢
	proveit.core_expr_types.lambda_maps.lambda_substitution
59	instantiation	115, 71	⊢
	: , : , :
60	instantiation	115, 72	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.division.div_rational_nonzero_closure
62	instantiation	131, 74, 73	⊢
	: , : , :
63	instantiation	131, 74, 75	⊢
	: , : , :
64	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
65	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
66	instantiation	131, 121, 76	⊢
	: , : , :
67	instantiation	77, 78, 79	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.multiplication.mult_zero_any
69	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
70	instantiation	80	⊢
	: , : , : , :
71	instantiation	115, 81	⊢
	: , : , :
72	instantiation	106, 82, 83	⊢
	: , : , :
73	instantiation	131, 85, 84	⊢
	: , : , :
74	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
75	instantiation	131, 85, 86	⊢
	: , : , :
76	instantiation	131, 123, 87	⊢
	: , : , :
77	theorem		⊢
	proveit.logic.equality.sub_right_side_into
78	instantiation	110, 96, 88	⊢
	: , :
79	instantiation	106, 89, 90	⊢
	: , : , :
80	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
81	instantiation	115, 91	⊢
	: , : , :
82	instantiation	115, 92	⊢
	: , : , :
83	instantiation	93, 94, 128, 95, 118, 111, 102, 103	⊢
	: , : , : , :
84	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
85	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
86	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
87	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
88	instantiation	110, 102, 103	⊢
	: , :
89	instantiation	97, 128, 133, 98, 101, 99, 96, 102, 103	⊢
	: , : , : , : , : , :
90	instantiation	97, 98, 133, 99, 100, 101, 118, 111, 102, 103	⊢
	: , : , : , : , : , :
91	instantiation	104, 105	⊢
	:
92	instantiation	106, 107, 108	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
94	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
95	instantiation	109	⊢
	: , : , :
96	instantiation	110, 118, 111	⊢
	: , :
97	theorem		⊢
	proveit.numbers.multiplication.disassociation
98	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
99	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
100	instantiation	112	⊢
	: , :
101	instantiation	112	⊢
	: , :
102	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
103	instantiation	131, 121, 113	⊢
	: , : , :
104	theorem		⊢
	proveit.numbers.addition.elim_zero_left
105	instantiation	131, 121, 114	⊢
	: , : , :
106	axiom		⊢
	proveit.logic.equality.equals_transitivity
107	instantiation	115, 116	⊢
	: , : , :
108	instantiation	117, 118	⊢
	:
109	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
110	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
111	instantiation	131, 121, 119	⊢
	: , : , :
112	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
113	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
114	instantiation	131, 126, 120	⊢
	: , : , :
115	axiom		⊢
	proveit.logic.equality.substitution
116	theorem		⊢
	proveit.numbers.negation.negated_zero
117	theorem		⊢
	proveit.numbers.exponentiation.exp_zero_eq_one
118	instantiation	131, 121, 122	⊢
	: , : , :
119	instantiation	131, 123, 124	⊢
	: , : , :
120	instantiation	131, 129, 125	⊢
	: , : , :
121	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
122	instantiation	131, 126, 127	⊢
	: , : , :
123	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
124	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
125	instantiation	131, 132, 128	⊢
	: , : , :
126	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
127	instantiation	131, 129, 130	⊢
	: , : , :
128	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
129	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
130	instantiation	131, 132, 133	⊢
	: , : , :
131	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
132	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
133	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements