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