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	52	⊢
2	instantiation	52, 4, 5, 6*	⊢
	: , : , :
3	instantiation	12, 7, 64	⊢
	: , :
4	instantiation	8, 9, 10, 15, 11*	⊢
	: , : , :
5	instantiation	12, 42, 65	⊢
	: , :
6	instantiation	13, 14, 15, 16, 17*	⊢
	: , :
7	instantiation	167, 140, 18	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.modular.mod_abs_of_difference_bound
9	instantiation	94, 73, 51	⊢
	: , :
10	instantiation	94, 73, 18	⊢
	: , :
11	instantiation	107, 19, 20	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.addition.commutation
13	theorem		⊢
	proveit.numbers.modular.mod_abs_x_reduce_to_abs_x
14	instantiation	94, 76, 51	⊢
	: , :
15	instantiation	21, 78, 141	⊢
	: , :
16	instantiation	22, 23	⊢
	: , :
17	instantiation	24, 25, 26*	⊢
	:
18	instantiation	60, 76	⊢
	:
19	instantiation	66, 27	⊢
	: , : , :
20	instantiation	28, 29, 30, 31	⊢
	: , : , : , :
21	theorem		⊢
	proveit.numbers.exponentiation.exp_real_pos_closure
22	theorem		⊢
	proveit.numbers.ordering.relax_less
23	instantiation	32, 33, 34	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.absolute_value.abs_neg_elim
25	instantiation	35, 36	⊢
	: , :
26	instantiation	37, 65, 64	⊢
	: , :
27	instantiation	37, 59, 65	⊢
	: , :
28	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
29	instantiation	119, 120, 164, 169, 122, 39, 59, 42, 38	⊢
	: , : , : , : , : , :
30	instantiation	119, 164, 120, 39, 40, 122, 59, 42, 50, 65	⊢
	: , : , : , : , : , :
31	instantiation	41, 120, 169, 122, 59, 42, 65, 43	⊢
	: , : , : , : , : , : , : , :
32	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
33	instantiation	44, 146, 147, 45	⊢
	: , : , :
34	instantiation	61, 46, 47	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.addition.subtraction.nonpos_difference
36	instantiation	48, 118	⊢
	:
37	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_subtract
38	instantiation	49, 50, 65	⊢
	: , :
39	instantiation	138	⊢
	: , :
40	instantiation	138	⊢
	: , :
41	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general
42	instantiation	167, 140, 51	⊢
	: , : , :
43	instantiation	142	⊢
	:
44	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
45	instantiation	52, 53, 54	⊢
	: , : , :
46	instantiation	55, 114	⊢
	:
47	instantiation	107, 56, 57	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.rounding.floor_x_le_x
49	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
50	instantiation	58, 59	⊢
	:
51	instantiation	60, 118	⊢
	:
52	theorem		⊢
	proveit.logic.equality.sub_right_side_into
53	instantiation	61, 90, 62	⊢
	: , : , :
54	instantiation	63, 64, 65	⊢
	: , :
55	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
56	instantiation	66, 67	⊢
	: , : , :
57	instantiation	68, 69, 70, 87, 71*, 72*	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.negation.complex_closure
59	instantiation	167, 140, 73	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.negation.real_closure
61	theorem		⊢
	proveit.logic.equality.sub_left_side_into
62	instantiation	74, 75	⊢
	:
63	theorem		⊢
	proveit.numbers.absolute_value.abs_diff_reversal
64	instantiation	167, 140, 118	⊢
	: , : , :
65	instantiation	167, 140, 76	⊢
	: , : , :
66	axiom		⊢
	proveit.logic.equality.substitution
67	instantiation	77, 78, 141, 147, 79, 80, 81*	⊢
	: , : , : , :
68	theorem		⊢
	proveit.numbers.division.frac_cancel_left
69	instantiation	167, 83, 82	⊢
	: , : , :
70	instantiation	167, 83, 84	⊢
	: , : , :
71	instantiation	85, 98	⊢
	:
72	instantiation	86, 87	⊢
	:
73	instantiation	167, 153, 88	⊢
	: , : , :
74	theorem		⊢
	proveit.numbers.absolute_value.abs_non_neg_elim
75	instantiation	89, 146, 147, 90	⊢
	: , : , :
76	instantiation	167, 153, 91	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.exponentiation.exp_factored_real
78	instantiation	167, 92, 93	⊢
	: , : , :
79	instantiation	94, 141, 139	⊢
	: , :
80	instantiation	95, 96	⊢
	: , :
81	instantiation	97, 98	⊢
	:
82	instantiation	167, 100, 99	⊢
	: , : , :
83	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
84	instantiation	167, 100, 101	⊢
	: , : , :
85	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
86	theorem		⊢
	proveit.numbers.division.frac_one_denom
87	instantiation	167, 140, 102	⊢
	: , : , :
88	instantiation	167, 161, 103	⊢
	: , : , :
89	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
90	instantiation	104, 118	⊢
	:
91	instantiation	167, 161, 105	⊢
	: , : , :
92	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
93	instantiation	167, 106, 129	⊢
	: , : , :
94	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
95	theorem		⊢
	proveit.logic.equality.equals_reversal
96	instantiation	107, 108, 109	⊢
	: , : , :
97	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
98	instantiation	167, 140, 110	⊢
	: , : , :
99	instantiation	167, 112, 111	⊢
	: , : , :
100	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
101	instantiation	167, 112, 113	⊢
	: , : , :
102	instantiation	150, 151, 114	⊢
	: , : , :
103	instantiation	167, 115, 116	⊢
	: , : , :
104	theorem		⊢
	proveit.numbers.rounding.real_minus_floor_interval
105	instantiation	117, 118	⊢
	:
106	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
107	axiom		⊢
	proveit.logic.equality.equals_transitivity
108	instantiation	119, 169, 164, 120, 121, 122, 125, 126, 123	⊢
	: , : , : , : , : , :
109	instantiation	124, 125, 126, 127	⊢
	: , : , :
110	instantiation	167, 153, 128	⊢
	: , : , :
111	instantiation	167, 130, 129	⊢
	: , : , :
112	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
113	instantiation	167, 130, 131	⊢
	: , : , :
114	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
115	instantiation	132, 133, 134	⊢
	: , :
116	assumption		⊢
117	axiom		⊢
	proveit.numbers.rounding.floor_is_an_int
118	instantiation	135, 136, 137	⊢
	: , :
119	theorem		⊢
	proveit.numbers.addition.disassociation
120	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
121	instantiation	138	⊢
	: , :
122	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
123	instantiation	167, 140, 139	⊢
	: , : , :
124	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
125	instantiation	167, 140, 147	⊢
	: , : , :
126	instantiation	167, 140, 141	⊢
	: , : , :
127	instantiation	142	⊢
	:
128	instantiation	167, 161, 159	⊢
	: , : , :
129	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
130	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
131	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
132	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
133	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
134	instantiation	143, 152, 155	⊢
	: , :
135	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
136	instantiation	167, 153, 144	⊢
	: , : , :
137	instantiation	145, 146, 147, 148	⊢
	: , : , :
138	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
139	instantiation	167, 153, 149	⊢
	: , : , :
140	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
141	instantiation	150, 151, 166	⊢
	: , : , :
142	axiom		⊢
	proveit.logic.equality.equals_reflexivity
143	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
144	instantiation	167, 161, 152	⊢
	: , : , :
145	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
146	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
147	instantiation	167, 153, 154	⊢
	: , : , :
148	axiom		⊢
	proveit.physics.quantum.QPE._phase_in_interval
149	instantiation	167, 161, 155	⊢
	: , : , :
150	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
151	instantiation	156, 157	⊢
	: , :
152	instantiation	158, 159, 160	⊢
	: , :
153	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
154	instantiation	167, 161, 163	⊢
	: , : , :
155	instantiation	162, 163	⊢
	:
156	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
157	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
158	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
159	instantiation	167, 168, 164	⊢
	: , : , :
160	instantiation	167, 165, 166	⊢
	: , : , :
161	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
162	theorem		⊢
	proveit.numbers.negation.int_closure
163	instantiation	167, 168, 169	⊢
	: , : , :
164	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
165	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
166	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
167	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
168	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
169	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements