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