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, 5, 6*	⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.addition.weak_bound_via_right_term_bound
2	reference	42	⊢
3	instantiation	118, 33, 32	⊢
	: , :
4	reference	171	⊢
5	instantiation	7, 8, 9	⊢
	: , : , :
6	instantiation	131, 10, 11	⊢
	: , : , :
7	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less_eq
8	instantiation	75, 12, 13, 14*	⊢
	: , : , :
9	instantiation	85, 15, 16	⊢
	: , : , :
10	instantiation	143, 193, 188, 144, 17, 146, 19, 20, 18	⊢
	: , : , : , : , : , :
11	instantiation	148, 19, 20, 21	⊢
	: , : , :
12	instantiation	22, 43, 55, 26, 23*	⊢
	: , : , :
13	instantiation	30, 62, 89	⊢
	: , :
14	instantiation	24, 25, 26, 27, 28*	⊢
	: , :
15	instantiation	37, 29	⊢
	: , :
16	instantiation	30, 31, 88	⊢
	: , :
17	instantiation	162	⊢
	: , :
18	instantiation	191, 164, 32	⊢
	: , : , :
19	instantiation	191, 164, 42	⊢
	: , : , :
20	instantiation	191, 164, 33	⊢
	: , : , :
21	instantiation	166	⊢
	:
22	theorem		⊢
	proveit.numbers.modular.mod_abs_of_difference_bound
23	instantiation	131, 34, 35	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.modular.mod_abs_x_reduce_to_abs_x
25	instantiation	118, 100, 74	⊢
	: , :
26	instantiation	36, 102, 165	⊢
	: , :
27	instantiation	37, 38	⊢
	: , :
28	instantiation	39, 40, 41*	⊢
	:
29	instantiation	64, 170, 171, 114	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.addition.commutation
31	instantiation	191, 164, 69	⊢
	: , : , :
32	instantiation	84, 42	⊢
	:
33	instantiation	54, 43, 160, 56	⊢
	: , :
34	instantiation	90, 44	⊢
	: , : , :
35	instantiation	45, 46, 47, 48	⊢
	: , : , : , :
36	theorem		⊢
	proveit.numbers.exponentiation.exp_real_pos_closure
37	theorem		⊢
	proveit.numbers.ordering.relax_less
38	instantiation	49, 50, 51	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.absolute_value.abs_neg_elim
40	instantiation	52, 53	⊢
	: , :
41	instantiation	57, 89, 88	⊢
	: , :
42	instantiation	54, 55, 160, 56	⊢
	: , :
43	instantiation	118, 97, 74	⊢
	: , :
44	instantiation	57, 83, 89	⊢
	: , :
45	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
46	instantiation	143, 144, 188, 193, 146, 59, 83, 62, 58	⊢
	: , : , : , : , : , :
47	instantiation	143, 188, 144, 59, 60, 146, 83, 62, 73, 89	⊢
	: , : , : , : , : , :
48	instantiation	61, 144, 193, 146, 83, 62, 89, 63	⊢
	: , : , : , : , : , : , : , :
49	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
50	instantiation	64, 170, 171, 65	⊢
	: , : , :
51	instantiation	85, 66, 67	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.addition.subtraction.nonpos_difference
53	instantiation	68, 142	⊢
	:
54	theorem		⊢
	proveit.numbers.modular.mod_abs_real_closure
55	instantiation	118, 97, 69	⊢
	: , :
56	instantiation	70, 123, 71	⊢
	: , :
57	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_subtract
58	instantiation	72, 73, 89	⊢
	: , :
59	instantiation	162	⊢
	: , :
60	instantiation	162	⊢
	: , :
61	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general
62	instantiation	191, 164, 74	⊢
	: , : , :
63	instantiation	166	⊢
	:
64	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
65	instantiation	75, 76, 77	⊢
	: , : , :
66	instantiation	78, 138	⊢
	:
67	instantiation	131, 79, 80	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.rounding.floor_x_le_x
69	instantiation	84, 100	⊢
	:
70	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
71	instantiation	191, 136, 81	⊢
	: , : , :
72	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
73	instantiation	82, 83	⊢
	:
74	instantiation	84, 142	⊢
	:
75	theorem		⊢
	proveit.logic.equality.sub_right_side_into
76	instantiation	85, 114, 86	⊢
	: , : , :
77	instantiation	87, 88, 89	⊢
	: , :
78	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
79	instantiation	90, 91	⊢
	: , : , :
80	instantiation	92, 93, 94, 111, 95*, 96*	⊢
	: , : , :
81	instantiation	191, 154, 190	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.negation.complex_closure
83	instantiation	191, 164, 97	⊢
	: , : , :
84	theorem		⊢
	proveit.numbers.negation.real_closure
85	theorem		⊢
	proveit.logic.equality.sub_left_side_into
86	instantiation	98, 99	⊢
	:
87	theorem		⊢
	proveit.numbers.absolute_value.abs_diff_reversal
88	instantiation	191, 164, 142	⊢
	: , : , :
89	instantiation	191, 164, 100	⊢
	: , : , :
90	axiom		⊢
	proveit.logic.equality.substitution
91	instantiation	101, 102, 165, 171, 103, 104, 105*	⊢
	: , : , : , :
92	theorem		⊢
	proveit.numbers.division.frac_cancel_left
93	instantiation	191, 107, 106	⊢
	: , : , :
94	instantiation	191, 107, 108	⊢
	: , : , :
95	instantiation	109, 122	⊢
	:
96	instantiation	110, 111	⊢
	:
97	instantiation	191, 177, 112	⊢
	: , : , :
98	theorem		⊢
	proveit.numbers.absolute_value.abs_non_neg_elim
99	instantiation	113, 170, 171, 114	⊢
	: , : , :
100	instantiation	191, 177, 115	⊢
	: , : , :
101	theorem		⊢
	proveit.numbers.exponentiation.exp_factored_real
102	instantiation	191, 116, 117	⊢
	: , : , :
103	instantiation	118, 165, 163	⊢
	: , :
104	instantiation	119, 120	⊢
	: , :
105	instantiation	121, 122	⊢
	:
106	instantiation	191, 124, 123	⊢
	: , : , :
107	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
108	instantiation	191, 124, 125	⊢
	: , : , :
109	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
110	theorem		⊢
	proveit.numbers.division.frac_one_denom
111	instantiation	191, 164, 126	⊢
	: , : , :
112	instantiation	191, 185, 127	⊢
	: , : , :
113	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
114	instantiation	128, 142	⊢
	:
115	instantiation	191, 185, 129	⊢
	: , : , :
116	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
117	instantiation	191, 130, 153	⊢
	: , : , :
118	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
119	theorem		⊢
	proveit.logic.equality.equals_reversal
120	instantiation	131, 132, 133	⊢
	: , : , :
121	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
122	instantiation	191, 164, 134	⊢
	: , : , :
123	instantiation	191, 136, 135	⊢
	: , : , :
124	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
125	instantiation	191, 136, 137	⊢
	: , : , :
126	instantiation	174, 175, 138	⊢
	: , : , :
127	instantiation	191, 139, 140	⊢
	: , : , :
128	theorem		⊢
	proveit.numbers.rounding.real_minus_floor_interval
129	instantiation	141, 142	⊢
	:
130	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
131	axiom		⊢
	proveit.logic.equality.equals_transitivity
132	instantiation	143, 193, 188, 144, 145, 146, 149, 150, 147	⊢
	: , : , : , : , : , :
133	instantiation	148, 149, 150, 151	⊢
	: , : , :
134	instantiation	191, 177, 152	⊢
	: , : , :
135	instantiation	191, 154, 153	⊢
	: , : , :
136	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
137	instantiation	191, 154, 155	⊢
	: , : , :
138	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
139	instantiation	156, 157, 158	⊢
	: , :
140	assumption		⊢
141	axiom		⊢
	proveit.numbers.rounding.floor_is_an_int
142	instantiation	159, 160, 161	⊢
	: , :
143	theorem		⊢
	proveit.numbers.addition.disassociation
144	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
145	instantiation	162	⊢
	: , :
146	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
147	instantiation	191, 164, 163	⊢
	: , : , :
148	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
149	instantiation	191, 164, 171	⊢
	: , : , :
150	instantiation	191, 164, 165	⊢
	: , : , :
151	instantiation	166	⊢
	:
152	instantiation	191, 185, 183	⊢
	: , : , :
153	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
154	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
155	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
156	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
157	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
158	instantiation	167, 176, 179	⊢
	: , :
159	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
160	instantiation	191, 177, 168	⊢
	: , : , :
161	instantiation	169, 170, 171, 172	⊢
	: , : , :
162	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
163	instantiation	191, 177, 173	⊢
	: , : , :
164	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
165	instantiation	174, 175, 190	⊢
	: , : , :
166	axiom		⊢
	proveit.logic.equality.equals_reflexivity
167	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
168	instantiation	191, 185, 176	⊢
	: , : , :
169	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
170	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
171	instantiation	191, 177, 178	⊢
	: , : , :
172	axiom		⊢
	proveit.physics.quantum.QPE._phase_in_interval
173	instantiation	191, 185, 179	⊢
	: , : , :
174	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
175	instantiation	180, 181	⊢
	: , :
176	instantiation	182, 183, 184	⊢
	: , :
177	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
178	instantiation	191, 185, 187	⊢
	: , : , :
179	instantiation	186, 187	⊢
	:
180	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
181	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
182	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
183	instantiation	191, 192, 188	⊢
	: , : , :
184	instantiation	191, 189, 190	⊢
	: , : , :
185	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
186	theorem		⊢
	proveit.numbers.negation.int_closure
187	instantiation	191, 192, 193	⊢
	: , : , :
188	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
189	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
190	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
191	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
192	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
193	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements