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	115	⊢
2	instantiation	126, 4	⊢
	: , : , :
3	instantiation	115, 5, 6	⊢
	: , : , :
4	instantiation	7, 135, 98, 74, 49, 56, 8*	⊢
	: , : , :
5	instantiation	115, 9, 10	⊢
	: , : , :
6	instantiation	115, 11, 12	⊢
	: , : , :
7	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_product
8	instantiation	13, 86, 133, 14*	⊢
	: , :
9	instantiation	115, 15, 16	⊢
	: , : , :
10	instantiation	115, 17, 18	⊢
	: , : , :
11	instantiation	60, 61, 33, 62, 35, 98, 42, 41	⊢
	: , : , : , :
12	instantiation	115, 19, 20	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
14	instantiation	80, 135	⊢
	:
15	instantiation	59, 61, 33, 160, 62, 23, 135, 98, 42, 21	⊢
	: , : , : , : , : , :
16	instantiation	59, 33, 162, 61, 23, 22, 62, 135, 98, 42, 36, 41	⊢
	: , : , : , : , : , :
17	instantiation	38, 61, 33, 160, 62, 23, 135, 98, 42, 36, 41	⊢
	: , : , : , : , : , : , :
18	instantiation	115, 24, 25	⊢
	: , : , :
19	instantiation	115, 26, 27	⊢
	: , : , :
20	instantiation	28, 160, 61, 62, 109, 44, 29, 30*, 31*	⊢
	: , : , : , : , : , :
21	instantiation	32, 36, 41	⊢
	: , :
22	instantiation	83	⊢
	: , :
23	instantiation	47	⊢
	: , : , :
24	instantiation	39, 61, 162, 33, 62, 34, 35, 36, 135, 98, 42, 41	⊢
	: , : , : , : , : , :
25	instantiation	126, 37	⊢
	: , : , :
26	instantiation	38, 160, 61, 62, 98, 42, 41	⊢
	: , : , : , : , : , : , :
27	instantiation	39, 61, 162, 160, 62, 40, 98, 41, 42, 43*	⊢
	: , : , : , : , : , :
28	theorem		⊢
	proveit.numbers.multiplication.distribute_through_subtract
29	instantiation	163, 141, 94	⊢
	: , : , :
30	instantiation	125, 44	⊢
	:
31	instantiation	115, 45, 46	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
33	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
34	instantiation	83	⊢
	: , :
35	instantiation	47	⊢
	: , : , :
36	instantiation	48, 109, 135, 49	⊢
	: , :
37	instantiation	67, 50, 51	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
39	theorem		⊢
	proveit.numbers.multiplication.association
40	instantiation	83	⊢
	: , :
41	instantiation	52, 98, 53	⊢
	: , :
42	instantiation	163, 141, 54	⊢
	: , : , :
43	instantiation	55, 98, 120, 74, 56, 57*, 58*	⊢
	: , : , :
44	instantiation	163, 141, 76	⊢
	: , : , :
45	instantiation	59, 160, 162, 61, 63, 62, 109, 64, 65	⊢
	: , : , : , : , : , :
46	instantiation	60, 61, 162, 62, 63, 64, 65	⊢
	: , : , : , :
47	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
48	theorem		⊢
	proveit.numbers.division.div_complex_closure
49	instantiation	66, 154	⊢
	:
50	instantiation	67, 68, 69	⊢
	: , : , :
51	instantiation	70, 71, 72, 73	⊢
	: , : , : , :
52	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
53	instantiation	163, 141, 74	⊢
	: , : , :
54	instantiation	75, 76, 77	⊢
	: , :
55	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
56	instantiation	78, 79	⊢
	:
57	instantiation	80, 98	⊢
	:
58	instantiation	115, 81, 82	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.multiplication.disassociation
60	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
61	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
62	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
63	instantiation	83	⊢
	: , :
64	instantiation	163, 141, 106	⊢
	: , : , :
65	instantiation	163, 141, 107	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
67	theorem		⊢
	proveit.logic.equality.sub_right_side_into
68	instantiation	84, 109, 85, 86	⊢
	: , : , : , : , :
69	instantiation	115, 87, 88	⊢
	: , : , :
70	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
71	instantiation	126, 89	⊢
	: , : , :
72	instantiation	126, 89	⊢
	: , : , :
73	instantiation	134, 109	⊢
	:
74	instantiation	163, 148, 90	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
76	instantiation	91, 92	⊢
	:
77	instantiation	93, 94	⊢
	:
78	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
79	instantiation	163, 95, 123	⊢
	: , : , :
80	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
81	instantiation	126, 96	⊢
	: , : , :
82	instantiation	97, 98	⊢
	:
83	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
84	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_denom_left
85	instantiation	163, 100, 99	⊢
	: , : , :
86	instantiation	163, 100, 101	⊢
	: , : , :
87	instantiation	126, 102	⊢
	: , : , :
88	instantiation	126, 103	⊢
	: , : , :
89	instantiation	128, 109	⊢
	:
90	instantiation	163, 156, 104	⊢
	: , : , :
91	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
92	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
93	theorem		⊢
	proveit.numbers.negation.real_closure
94	instantiation	105, 106, 107	⊢
	: , :
95	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
96	instantiation	108, 109, 110	⊢
	: , :
97	theorem		⊢
	proveit.numbers.exponentiation.exp_zero_eq_one
98	instantiation	163, 141, 111	⊢
	: , : , :
99	instantiation	163, 113, 112	⊢
	: , : , :
100	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
101	instantiation	163, 113, 139	⊢
	: , : , :
102	instantiation	126, 114	⊢
	: , : , :
103	instantiation	115, 116, 117	⊢
	: , : , :
104	instantiation	158, 152	⊢
	:
105	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
106	instantiation	163, 148, 118	⊢
	: , : , :
107	instantiation	163, 148, 119	⊢
	: , : , :
108	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
109	instantiation	163, 141, 120	⊢
	: , : , :
110	instantiation	121	⊢
	:
111	instantiation	163, 122, 123	⊢
	: , : , :
112	instantiation	163, 145, 124	⊢
	: , : , :
113	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
114	instantiation	125, 135	⊢
	:
115	axiom		⊢
	proveit.logic.equality.equals_transitivity
116	instantiation	126, 127	⊢
	: , : , :
117	instantiation	128, 135	⊢
	:
118	instantiation	163, 156, 129	⊢
	: , : , :
119	instantiation	163, 130, 131	⊢
	: , : , :
120	instantiation	163, 148, 132	⊢
	: , : , :
121	axiom		⊢
	proveit.logic.equality.equals_reflexivity
122	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
123	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
124	instantiation	163, 153, 133	⊢
	: , : , :
125	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
126	axiom		⊢
	proveit.logic.equality.substitution
127	instantiation	134, 135	⊢
	:
128	theorem		⊢
	proveit.numbers.division.frac_one_denom
129	instantiation	163, 136, 137	⊢
	: , : , :
130	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational
131	instantiation	138, 139, 140	⊢
	: , :
132	instantiation	163, 156, 152	⊢
	: , : , :
133	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
134	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
135	instantiation	163, 141, 142	⊢
	: , : , :
136	instantiation	143, 144, 159	⊢
	: , :
137	assumption		⊢
138	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_nonzero_closure
139	instantiation	163, 145, 146	⊢
	: , : , :
140	instantiation	158, 147	⊢
	:
141	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
142	instantiation	163, 148, 149	⊢
	: , : , :
143	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
144	instantiation	150, 151, 152	⊢
	: , :
145	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
146	instantiation	163, 153, 154	⊢
	: , : , :
147	instantiation	163, 164, 155	⊢
	: , : , :
148	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
149	instantiation	163, 156, 157	⊢
	: , : , :
150	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
151	instantiation	158, 159	⊢
	:
152	instantiation	163, 161, 160	⊢
	: , : , :
153	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
154	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
155	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
156	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
157	instantiation	163, 161, 162	⊢
	: , : , :
158	theorem		⊢
	proveit.numbers.negation.int_closure
159	instantiation	163, 164, 165	⊢
	: , : , :
160	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
161	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
162	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
163	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
164	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
165	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
*equality replacement requirements