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	⊢
	: , :
1	theorem		⊢
	proveit.numbers.addition.subtraction.nonneg_difference
2	instantiation	40, 44, 150, 3, 4, 5*, 6*	⊢
	: , : , :
3	instantiation	64, 8, 150	⊢
	: , :
4	instantiation	7, 150, 8, 9, 123	⊢
	: , : , :
5	instantiation	126, 10, 11	⊢
	: , : , :
6	instantiation	126, 12, 13	⊢
	: , : , :
7	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right
8	instantiation	64, 66, 110	⊢
	: , :
9	instantiation	24, 14, 15	⊢
	: , : , :
10	instantiation	82, 204, 175, 83, 30, 84, 139, 88, 31	⊢
	: , : , : , : , : , :
11	instantiation	87, 139, 88, 49	⊢
	: , : , :
12	instantiation	96, 16	⊢
	: , : , :
13	instantiation	17, 18, 19, 20	⊢
	: , : , : , :
14	instantiation	21, 201, 38, 22, 23*	⊢
	: , :
15	instantiation	24, 25, 26	⊢
	: , : , :
16	instantiation	82, 83, 175, 204, 84, 48, 51, 86, 139	⊢
	: , : , : , : , : , :
17	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
18	instantiation	82, 83, 28, 204, 84, 29, 51, 86, 139, 27	⊢
	: , : , : , : , : , :
19	instantiation	82, 28, 175, 83, 29, 30, 84, 51, 86, 139, 88, 31	⊢
	: , : , : , : , : , :
20	instantiation	126, 32, 33	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.rounding.ceil_of_real_above_int
22	instantiation	34, 184, 60, 35, 176, 36*	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
24	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less_eq
25	instantiation	37, 38, 157, 39	⊢
	: , :
26	instantiation	40, 110, 41, 66, 42, 43*	⊢
	: , : , :
27	instantiation	202, 161, 44	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
29	instantiation	45	⊢
	: , : , :
30	instantiation	151	⊢
	: , :
31	instantiation	46, 139	⊢
	:
32	instantiation	47, 175, 204, 83, 48, 84, 51, 86, 139, 88, 49	⊢
	: , : , : , : , : , : , : , :
33	instantiation	50, 88, 51, 90	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.logarithms.log_increasing_less
35	instantiation	52, 150, 53, 54, 55, 56*, 57*	⊢
	: , : , :
36	instantiation	58, 184	⊢
	:
37	theorem		⊢
	proveit.numbers.rounding.ceil_increasing_less_eq
38	instantiation	162, 184, 60, 164	⊢
	: , :
39	instantiation	59, 184, 60, 163, 61, 176	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
41	instantiation	64, 131, 111	⊢
	: , :
42	axiom		⊢
	proveit.physics.quantum.QPE._t_req
43	instantiation	126, 62, 63	⊢
	: , : , :
44	instantiation	64, 131, 65	⊢
	: , :
45	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
46	theorem		⊢
	proveit.numbers.negation.complex_closure
47	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general
48	instantiation	151	⊢
	: , :
49	instantiation	112	⊢
	:
50	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
51	instantiation	202, 161, 66	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
53	instantiation	67, 133, 195	⊢
	: , :
54	instantiation	202, 198, 68	⊢
	: , : , :
55	instantiation	69, 133, 195, 196, 70, 71	⊢
	: , : , :
56	instantiation	126, 72, 73	⊢
	: , : , :
57	instantiation	126, 74, 75	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.logarithms.log_eq_1
59	theorem		⊢
	proveit.numbers.logarithms.log_increasing_less_eq
60	instantiation	171, 76, 184, 101	⊢
	: , :
61	instantiation	77, 150, 78, 79, 80, 81*	⊢
	: , : , :
62	instantiation	82, 83, 175, 204, 84, 85, 88, 89, 86	⊢
	: , : , : , : , : , :
63	instantiation	87, 88, 89, 90	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
65	instantiation	130, 150	⊢
	:
66	instantiation	145, 146, 91	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
68	instantiation	92, 149, 199	⊢
	: , :
69	theorem		⊢
	proveit.numbers.multiplication.strong_bound_via_right_factor_bound
70	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
71	instantiation	93, 159	⊢
	:
72	instantiation	96, 94	⊢
	: , : , :
73	instantiation	95, 139	⊢
	:
74	instantiation	96, 97	⊢
	: , : , :
75	instantiation	106, 201, 166, 107*, 98*, 124*	⊢
	: , : , : , :
76	instantiation	202, 186, 99	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.addition.weak_bound_via_right_term_bound
78	instantiation	100, 196, 150, 101	⊢
	: , :
79	instantiation	202, 102, 168	⊢
	: , : , :
80	instantiation	103, 104, 182, 184, 105	⊢
	: , : , :
81	instantiation	106, 166, 201, 107*, 108*, 109*	⊢
	: , : , : , :
82	theorem		⊢
	proveit.numbers.addition.disassociation
83	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
84	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
85	instantiation	151	⊢
	: , :
86	instantiation	202, 161, 110	⊢
	: , : , :
87	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
88	instantiation	202, 161, 131	⊢
	: , : , :
89	instantiation	202, 161, 111	⊢
	: , : , :
90	instantiation	112	⊢
	:
91	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
92	theorem		⊢
	proveit.numbers.multiplication.mult_rational_closure_bin
93	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
94	instantiation	113, 114	⊢
	:
95	theorem		⊢
	proveit.numbers.addition.elim_zero_left
96	axiom		⊢
	proveit.logic.equality.substitution
97	instantiation	152, 114	⊢
	:
98	instantiation	126, 115, 116	⊢
	: , : , :
99	instantiation	202, 191, 117	⊢
	: , : , :
100	theorem		⊢
	proveit.numbers.division.div_real_closure
101	instantiation	118, 192	⊢
	:
102	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
103	theorem		⊢
	proveit.numbers.division.weak_div_from_denom_bound__all_pos
104	instantiation	202, 119, 120	⊢
	: , : , :
105	instantiation	121, 150, 189, 196, 122, 123, 124*	⊢
	: , : , :
106	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
107	instantiation	125, 139	⊢
	:
108	instantiation	126, 127, 128	⊢
	: , : , :
109	instantiation	129, 139	⊢
	:
110	instantiation	130, 131	⊢
	:
111	instantiation	202, 198, 132	⊢
	: , : , :
112	axiom		⊢
	proveit.logic.equality.equals_reflexivity
113	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
114	instantiation	202, 161, 133	⊢
	: , : , :
115	instantiation	140, 175, 134, 135, 144, 143	⊢
	: , : , : , :
116	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_4
117	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
118	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
119	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg
120	instantiation	202, 136, 204	⊢
	: , : , :
121	theorem		⊢
	proveit.numbers.multiplication.weak_bound_via_right_factor_bound
122	instantiation	137, 195, 196, 197	⊢
	: , : , :
123	instantiation	138, 175	⊢
	:
124	instantiation	152, 139	⊢
	:
125	theorem		⊢
	proveit.numbers.division.frac_one_denom
126	axiom		⊢
	proveit.logic.equality.equals_transitivity
127	instantiation	140, 175, 141, 142, 143, 144	⊢
	: , : , : , :
128	theorem		⊢
	proveit.numbers.numerals.decimals.add_4_1
129	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
130	theorem		⊢
	proveit.numbers.negation.real_closure
131	instantiation	145, 146, 147	⊢
	: , : , :
132	instantiation	202, 200, 148	⊢
	: , : , :
133	instantiation	202, 198, 149	⊢
	: , : , :
134	instantiation	151	⊢
	: , :
135	instantiation	151	⊢
	: , :
136	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg
137	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_upper_bound
138	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
139	instantiation	202, 161, 150	⊢
	: , : , :
140	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
141	instantiation	151	⊢
	: , :
142	instantiation	151	⊢
	: , :
143	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
144	instantiation	152, 153	⊢
	:
145	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
146	instantiation	154, 155	⊢
	: , :
147	axiom		⊢
	proveit.physics.quantum.QPE._n_in_natural_pos
148	instantiation	156, 157	⊢
	:
149	instantiation	202, 158, 159	⊢
	: , : , :
150	instantiation	202, 198, 160	⊢
	: , : , :
151	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
152	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
153	instantiation	202, 161, 196	⊢
	: , : , :
154	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
155	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
156	axiom		⊢
	proveit.numbers.rounding.ceil_is_an_int
157	instantiation	162, 184, 163, 164	⊢
	: , :
158	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
159	instantiation	165, 177, 187	⊢
	: , :
160	instantiation	202, 200, 166	⊢
	: , : , :
161	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
162	theorem		⊢
	proveit.numbers.logarithms.log_real_pos_real_closure
163	instantiation	167, 184, 168	⊢
	: , :
164	instantiation	169, 170	⊢
	: , :
165	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
166	instantiation	202, 203, 175	⊢
	: , : , :
167	theorem		⊢
	proveit.numbers.addition.add_real_pos_closure_bin
168	instantiation	171, 172, 182, 173	⊢
	: , :
169	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
170	instantiation	174, 204, 175, 176	⊢
	: , :
171	theorem		⊢
	proveit.numbers.division.div_real_pos_closure
172	instantiation	202, 186, 177	⊢
	: , : , :
173	instantiation	178, 179	⊢
	:
174	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
175	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
176	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
177	instantiation	202, 191, 180	⊢
	: , : , :
178	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
179	instantiation	202, 181, 182	⊢
	: , : , :
180	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
181	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
182	instantiation	183, 184, 185	⊢
	: , :
183	theorem		⊢
	proveit.numbers.multiplication.mult_real_pos_closure_bin
184	instantiation	202, 186, 187	⊢
	: , : , :
185	instantiation	188, 189, 190	⊢
	:
186	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
187	instantiation	202, 191, 192	⊢
	: , : , :
188	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
189	instantiation	193, 195, 196, 197	⊢
	: , : , :
190	instantiation	194, 195, 196, 197	⊢
	: , : , :
191	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
192	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
193	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
194	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
195	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
196	instantiation	202, 198, 199	⊢
	: , : , :
197	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
198	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
199	instantiation	202, 200, 201	⊢
	: , : , :
200	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
201	instantiation	202, 203, 204	⊢
	: , : , :
202	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
203	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
204	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements