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	14	⊢
2	reference	15	⊢
3	instantiation	35, 105, 5, 6	⊢
	: , :
4	instantiation	7, 15, 8, 9	⊢
	: , : , : , :
5	instantiation	24, 122, 10	⊢
	: , :
6	instantiation	11, 12, 13	⊢
	: , : , :
7	theorem		⊢
	proveit.linear_algebra.addition.binary_closure
8	theorem		⊢
	proveit.physics.quantum.algebra.ket_zero_in_qubit_space
9	instantiation	14, 15, 16, 17	⊢
	: , : , : , :
10	instantiation	103, 18, 19	⊢
	: , :
11	theorem		⊢
	proveit.logic.equality.sub_left_side_into
12	instantiation	20, 130, 21	⊢
	: , :
13	instantiation	98, 22	⊢
	: , : , :
14	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
15	instantiation	23, 151	⊢
	:
16	instantiation	24, 25, 26	⊢
	: , :
17	theorem		⊢
	proveit.physics.quantum.algebra.ket_one_in_qubit_space
18	instantiation	35, 92, 122, 73	⊢
	: , :
19	instantiation	61, 27	⊢
	:
20	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
21	instantiation	28, 29, 130	⊢
	: , :
22	instantiation	84, 30, 31	⊢
	: , : , :
23	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
24	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
25	instantiation	152, 131, 32	⊢
	: , : , :
26	instantiation	52, 33, 34	⊢
	: , : , :
27	instantiation	35, 104, 122, 73	⊢
	: , :
28	theorem		⊢
	proveit.numbers.division.div_rational_nonzero_closure
29	instantiation	152, 138, 36	⊢
	: , : , :
30	instantiation	84, 37, 38	⊢
	: , : , :
31	instantiation	84, 39, 40	⊢
	: , : , :
32	instantiation	152, 90, 41	⊢
	: , : , :
33	instantiation	76, 55, 42	⊢
	: , :
34	instantiation	84, 43, 44	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.division.div_complex_closure
36	instantiation	152, 146, 149	⊢
	: , : , :
37	instantiation	98, 45	⊢
	: , : , :
38	instantiation	98, 46	⊢
	: , : , :
39	instantiation	47, 94, 154, 142, 96, 48, 62, 108, 49	⊢
	: , : , : , : , : , :
40	instantiation	50, 62, 108, 51	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
42	instantiation	52, 53, 54	⊢
	: , : , :
43	instantiation	65, 142, 56, 94, 58, 96, 55, 77, 78, 67	⊢
	: , : , : , : , : , :
44	instantiation	65, 94, 154, 56, 96, 57, 58, 122, 68, 77, 78, 67	⊢
	: , : , : , : , : , :
45	instantiation	72, 92, 122, 73, 59*	⊢
	: , :
46	instantiation	98, 60	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.addition.disassociation
48	instantiation	106	⊢
	: , :
49	instantiation	61, 62	⊢
	:
50	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
51	instantiation	63	⊢
	:
52	theorem		⊢
	proveit.logic.equality.sub_right_side_into
53	instantiation	76, 64, 67	⊢
	: , :
54	instantiation	65, 94, 154, 142, 96, 66, 77, 78, 67	⊢
	: , : , : , : , : , :
55	instantiation	76, 122, 68	⊢
	: , :
56	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
57	instantiation	106	⊢
	: , :
58	instantiation	69	⊢
	: , : , :
59	instantiation	84, 70, 71	⊢
	: , : , :
60	instantiation	72, 104, 122, 73, 74*	⊢
	: , :
61	theorem		⊢
	proveit.numbers.negation.complex_closure
62	instantiation	152, 131, 75	⊢
	: , : , :
63	axiom		⊢
	proveit.logic.equality.equals_reflexivity
64	instantiation	76, 77, 78	⊢
	: , :
65	theorem		⊢
	proveit.numbers.multiplication.disassociation
66	instantiation	106	⊢
	: , :
67	instantiation	152, 131, 79	⊢
	: , : , :
68	instantiation	152, 131, 80	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
70	instantiation	98, 99	⊢
	: , : , :
71	instantiation	84, 81, 82	⊢
	: , : , :
72	theorem		⊢
	proveit.numbers.division.div_as_mult
73	instantiation	83, 151	⊢
	:
74	instantiation	84, 85, 86	⊢
	: , : , :
75	instantiation	152, 140, 87	⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
77	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
78	instantiation	152, 131, 88	⊢
	: , : , :
79	instantiation	152, 140, 89	⊢
	: , : , :
80	instantiation	152, 90, 91	⊢
	: , : , :
81	instantiation	100, 92, 108	⊢
	: , :
82	instantiation	93, 142, 154, 94, 95, 96, 108, 104, 105, 97*	⊢
	: , : , : , : , : , :
83	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
84	axiom		⊢
	proveit.logic.equality.equals_transitivity
85	instantiation	98, 99	⊢
	: , : , :
86	instantiation	100, 104, 108	⊢
	: , :
87	instantiation	152, 136, 101	⊢
	: , : , :
88	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
89	instantiation	152, 147, 102	⊢
	: , : , :
90	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
91	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
92	instantiation	103, 104, 105	⊢
	: , :
93	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
94	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
95	instantiation	106	⊢
	: , :
96	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
97	instantiation	107, 108	⊢
	:
98	axiom		⊢
	proveit.logic.equality.substitution
99	instantiation	109, 110, 149, 111*	⊢
	: , :
100	theorem		⊢
	proveit.numbers.multiplication.commutation
101	instantiation	112, 137, 113	⊢
	: , :
102	instantiation	114, 148, 115	⊢
	: , :
103	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
104	instantiation	152, 131, 116	⊢
	: , : , :
105	instantiation	152, 131, 117	⊢
	: , : , :
106	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
107	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
108	instantiation	152, 131, 118	⊢
	: , : , :
109	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
110	instantiation	152, 119, 120	⊢
	: , : , :
111	instantiation	121, 122	⊢
	:
112	theorem		⊢
	proveit.numbers.multiplication.mult_rational_pos_closure_bin
113	instantiation	152, 150, 126	⊢
	: , : , :
114	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
115	instantiation	152, 123, 126	⊢
	: , : , :
116	instantiation	124, 125, 126	⊢
	: , : , :
117	instantiation	152, 140, 127	⊢
	: , : , :
118	instantiation	152, 140, 128	⊢
	: , : , :
119	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
120	instantiation	152, 129, 130	⊢
	: , : , :
121	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
122	instantiation	152, 131, 132	⊢
	: , : , :
123	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
124	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
125	instantiation	133, 134	⊢
	: , :
126	assumption		⊢
127	instantiation	152, 147, 135	⊢
	: , : , :
128	instantiation	152, 136, 137	⊢
	: , : , :
129	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
130	instantiation	152, 138, 139	⊢
	: , : , :
131	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
132	instantiation	152, 140, 141	⊢
	: , : , :
133	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
134	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
135	instantiation	152, 153, 142	⊢
	: , : , :
136	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
137	instantiation	143, 144, 145	⊢
	: , :
138	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
139	instantiation	152, 146, 151	⊢
	: , : , :
140	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
141	instantiation	152, 147, 148	⊢
	: , : , :
142	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
143	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
144	instantiation	152, 150, 149	⊢
	: , : , :
145	instantiation	152, 150, 151	⊢
	: , : , :
146	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
147	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
148	instantiation	152, 153, 154	⊢
	: , : , :
149	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
150	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
151	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
152	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
153	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
154	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements