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