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*, 7*	⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
2	instantiation	8, 83, 9, 10, 136, 66	⊢
	: , :
3	reference	109	⊢
4	instantiation	166, 153, 11	⊢
	: , : , :
5	instantiation	12, 152, 151, 142	⊢
	: , : , :
6	instantiation	78, 13, 14, 15	⊢
	: , : , : , :
7	instantiation	90, 16	⊢
	: , :
8	theorem		⊢
	proveit.numbers.addition.add_real_closure
9	instantiation	94	⊢
	: , : , :
10	instantiation	166, 153, 17	⊢
	: , : , :
11	instantiation	166, 161, 151	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
13	instantiation	56, 18, 19	⊢
	: , : , :
14	instantiation	73	⊢
	:
15	instantiation	90, 20	⊢
	: , :
16	instantiation	78, 21, 22, 23	⊢
	: , : , : , :
17	instantiation	166, 161, 24	⊢
	: , : , :
18	instantiation	92, 45	⊢
	: , : , :
19	instantiation	56, 25, 26	⊢
	: , : , :
20	instantiation	92, 55	⊢
	: , : , :
21	instantiation	27, 97, 125	⊢
	: , :
22	instantiation	90, 28	⊢
	: , :
23	instantiation	90, 29	⊢
	: , :
24	instantiation	164, 158	⊢
	:
25	instantiation	69, 160, 83, 70, 84, 72, 97, 85, 125, 86	⊢
	: , : , : , : , : , :
26	instantiation	59, 70, 168, 72, 30, 97, 85, 125, 53	⊢
	: , : , : , : , : , : , : , :
27	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
28	instantiation	31, 43, 97, 101, 32	⊢
	: , : , :
29	instantiation	56, 33, 34	⊢
	: , : , :
30	instantiation	87	⊢
	: , :
31	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
32	instantiation	62, 35, 36	⊢
	: , : , :
33	instantiation	56, 37, 38	⊢
	: , : , :
34	instantiation	56, 39, 40	⊢
	: , : , :
35	instantiation	56, 41, 42	⊢
	: , : , :
36	instantiation	99, 97, 43	⊢
	: , :
37	instantiation	92, 44	⊢
	: , : , :
38	instantiation	92, 45	⊢
	: , : , :
39	instantiation	56, 46, 47	⊢
	: , : , :
40	instantiation	48, 70, 168, 160, 72, 49, 76, 125, 86, 50*	⊢
	: , : , : , : , : , :
41	instantiation	69, 160, 168, 70, 51, 72, 97, 86, 101	⊢
	: , : , : , : , : , :
42	instantiation	52, 97, 101, 53	⊢
	: , : , :
43	instantiation	166, 146, 54	⊢
	: , : , :
44	instantiation	92, 67	⊢
	: , : , :
45	instantiation	92, 55	⊢
	: , : , :
46	instantiation	56, 57, 58	⊢
	: , : , :
47	instantiation	59, 70, 160, 168, 72, 60, 95, 76, 125, 86, 61	⊢
	: , : , : , : , : , : , : , :
48	theorem		⊢
	proveit.numbers.addition.association
49	instantiation	87	⊢
	: , :
50	instantiation	62, 63, 64	⊢
	: , : , :
51	instantiation	87	⊢
	: , :
52	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_12
53	instantiation	73	⊢
	:
54	instantiation	65, 66, 111	⊢
	: , :
55	instantiation	92, 67	⊢
	: , : , :
56	axiom		⊢
	proveit.logic.equality.equals_transitivity
57	instantiation	69, 70, 168, 160, 72, 71, 95, 76, 68	⊢
	: , : , : , : , : , :
58	instantiation	69, 168, 83, 70, 71, 84, 72, 95, 76, 85, 125, 86	⊢
	: , : , : , : , : , :
59	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general
60	instantiation	87	⊢
	: , :
61	instantiation	73	⊢
	:
62	theorem		⊢
	proveit.logic.equality.sub_right_side_into
63	instantiation	74, 125, 139, 75	⊢
	: , : , :
64	instantiation	99, 125, 76	⊢
	: , :
65	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
66	instantiation	77, 109	⊢
	:
67	instantiation	78, 79, 80, 81	⊢
	: , : , : , :
68	instantiation	82, 83, 84, 85, 125, 86	⊢
	: , :
69	theorem		⊢
	proveit.numbers.addition.disassociation
70	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
71	instantiation	87	⊢
	: , :
72	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
73	axiom		⊢
	proveit.logic.equality.equals_reflexivity
74	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add_reversed
75	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
76	instantiation	166, 146, 88	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.negation.real_closure
78	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
79	instantiation	92, 89	⊢
	: , : , :
80	instantiation	90, 91	⊢
	: , :
81	instantiation	92, 93	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.addition.add_complex_closure
83	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
84	instantiation	94	⊢
	: , : , :
85	instantiation	96, 95	⊢
	:
86	instantiation	96, 97	⊢
	:
87	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
88	instantiation	166, 153, 98	⊢
	: , : , :
89	instantiation	99, 100, 101	⊢
	: , :
90	theorem		⊢
	proveit.logic.equality.equals_reversal
91	instantiation	102, 139, 111, 110, 127	⊢
	: , : , :
92	axiom		⊢
	proveit.logic.equality.substitution
93	instantiation	103, 104, 105	⊢
	: , :
94	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
95	instantiation	106, 107, 108	⊢
	: , :
96	theorem		⊢
	proveit.numbers.negation.complex_closure
97	instantiation	166, 146, 109	⊢
	: , : , :
98	instantiation	166, 161, 159	⊢
	: , : , :
99	theorem		⊢
	proveit.numbers.addition.commutation
100	instantiation	166, 146, 110	⊢
	: , : , :
101	instantiation	166, 146, 111	⊢
	: , : , :
102	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
103	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
104	instantiation	166, 112, 113	⊢
	: , : , :
105	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
106	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
107	instantiation	114, 125, 115, 116	⊢
	: , :
108	instantiation	166, 146, 117	⊢
	: , : , :
109	instantiation	166, 153, 118	⊢
	: , : , :
110	instantiation	119, 120, 156	⊢
	: , : , :
111	instantiation	166, 153, 121	⊢
	: , : , :
112	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
113	instantiation	166, 122, 123	⊢
	: , : , :
114	theorem		⊢
	proveit.numbers.division.div_complex_closure
115	instantiation	124, 139, 125	⊢
	: , :
116	instantiation	126, 127, 128	⊢
	: , : , :
117	instantiation	166, 153, 129	⊢
	: , : , :
118	instantiation	166, 161, 130	⊢
	: , : , :
119	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
120	instantiation	131, 132	⊢
	: , :
121	instantiation	166, 161, 133	⊢
	: , : , :
122	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
123	instantiation	166, 134, 135	⊢
	: , : , :
124	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
125	instantiation	166, 146, 136	⊢
	: , : , :
126	theorem		⊢
	proveit.logic.equality.sub_left_side_into
127	instantiation	137, 144	⊢
	:
128	instantiation	138, 139	⊢
	:
129	instantiation	166, 161, 140	⊢
	: , : , :
130	instantiation	166, 141, 142	⊢
	: , : , :
131	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
132	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
133	instantiation	164, 152	⊢
	:
134	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
135	instantiation	166, 143, 144	⊢
	: , : , :
136	instantiation	166, 153, 145	⊢
	: , : , :
137	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
138	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
139	instantiation	166, 146, 147	⊢
	: , : , :
140	instantiation	148, 165, 149	⊢
	: , :
141	instantiation	150, 152, 151	⊢
	: , :
142	assumption		⊢
143	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
144	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
145	instantiation	166, 161, 152	⊢
	: , : , :
146	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
147	instantiation	166, 153, 154	⊢
	: , : , :
148	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
149	instantiation	166, 155, 156	⊢
	: , : , :
150	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
151	instantiation	157, 158, 159	⊢
	: , :
152	instantiation	166, 167, 160	⊢
	: , : , :
153	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
154	instantiation	166, 161, 165	⊢
	: , : , :
155	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
156	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
157	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
158	instantiation	166, 162, 163	⊢
	: , : , :
159	instantiation	164, 165	⊢
	:
160	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
161	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
162	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
163	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
164	theorem		⊢
	proveit.numbers.negation.int_closure
165	instantiation	166, 167, 168	⊢
	: , : , :
166	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
167	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
168	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements