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	⊢
	: , : , : , :
1	theorem		⊢
	proveit.numbers.number_sets.integers.interval_subset_eq
2	reference	37	⊢
3	instantiation	177, 6	⊢
	:
4	reference	171	⊢
5	instantiation	7, 103, 8, 9, 10, 11	⊢
	: , :
6	instantiation	170, 146, 167	⊢
	: , :
7	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_all
8	instantiation	114	⊢
	: , : , :
9	instantiation	12, 13, 14	⊢
	: , :
10	instantiation	15, 16, 128, 17, 18, 19*, 20*	⊢
	: , : , :
11	instantiation	21, 22	⊢
	: , :
12	theorem		⊢
	proveit.numbers.ordering.relax_equal_to_less_eq
13	instantiation	179, 168, 23	⊢
	: , : , :
14	instantiation	94	⊢
	:
15	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
16	instantiation	24, 103, 25, 26, 149, 27	⊢
	: , :
17	instantiation	179, 168, 28	⊢
	: , : , :
18	instantiation	29, 167, 166, 157	⊢
	: , : , :
19	instantiation	98, 30, 31, 32	⊢
	: , : , : , :
20	instantiation	110, 33	⊢
	: , :
21	theorem		⊢
	proveit.numbers.ordering.relax_less
22	instantiation	34, 35, 36	⊢
	: , : , :
23	instantiation	179, 174, 37	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.addition.add_real_closure
25	instantiation	114	⊢
	: , : , :
26	instantiation	179, 168, 38	⊢
	: , : , :
27	instantiation	130, 128	⊢
	:
28	instantiation	179, 174, 166	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
30	instantiation	78, 39, 40	⊢
	: , : , :
31	instantiation	94	⊢
	:
32	instantiation	110, 41	⊢
	: , :
33	instantiation	98, 42, 43, 44	⊢
	: , : , : , :
34	axiom		⊢
	proveit.numbers.ordering.transitivity_less_less
35	instantiation	45, 46	⊢
	:
36	instantiation	47, 176	⊢
	:
37	instantiation	170, 48, 167	⊢
	: , :
38	instantiation	179, 174, 48	⊢
	: , : , :
39	instantiation	112, 68	⊢
	: , : , :
40	instantiation	78, 49, 50	⊢
	: , : , :
41	instantiation	112, 77	⊢
	: , : , :
42	instantiation	51, 116, 141	⊢
	: , :
43	instantiation	118, 106, 119	⊢
	: , :
44	instantiation	110, 52	⊢
	: , :
45	theorem		⊢
	proveit.numbers.number_sets.integers.negative_if_in_neg_int
46	instantiation	53, 54	⊢
	:
47	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
48	instantiation	177, 171	⊢
	:
49	instantiation	90, 173, 103, 91, 104, 93, 116, 105, 141, 106	⊢
	: , : , : , : , : , :
50	instantiation	81, 91, 181, 93, 55, 116, 105, 141, 56	⊢
	: , : , : , : , : , : , : , :
51	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
52	instantiation	78, 57, 58	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.negation.int_neg_closure
54	instantiation	59, 60, 124	⊢
	: , :
55	instantiation	107	⊢
	: , :
56	instantiation	94	⊢
	:
57	instantiation	78, 61, 62	⊢
	: , : , :
58	instantiation	78, 63, 64	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
60	instantiation	65, 146, 66	⊢
	:
61	instantiation	112, 67	⊢
	: , : , :
62	instantiation	112, 68	⊢
	: , : , :
63	instantiation	78, 69, 70	⊢
	: , : , :
64	instantiation	71, 91, 181, 173, 93, 72, 97, 141, 106, 73*	⊢
	: , : , : , : , : , :
65	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
66	instantiation	74, 75, 76	⊢
	: , : , :
67	instantiation	112, 88	⊢
	: , : , :
68	instantiation	112, 77	⊢
	: , : , :
69	instantiation	78, 79, 80	⊢
	: , : , :
70	instantiation	81, 91, 173, 181, 93, 82, 115, 97, 141, 106, 83	⊢
	: , : , : , : , : , : , : , :
71	theorem		⊢
	proveit.numbers.addition.association
72	instantiation	107	⊢
	: , :
73	instantiation	84, 85, 86	⊢
	: , : , :
74	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
75	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
76	instantiation	87, 167, 166, 157	⊢
	: , : , :
77	instantiation	112, 88	⊢
	: , : , :
78	axiom		⊢
	proveit.logic.equality.equals_transitivity
79	instantiation	90, 91, 181, 173, 93, 92, 115, 97, 89	⊢
	: , : , : , : , : , :
80	instantiation	90, 181, 103, 91, 92, 104, 93, 115, 97, 105, 141, 106	⊢
	: , : , : , : , : , :
81	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general
82	instantiation	107	⊢
	: , :
83	instantiation	94	⊢
	:
84	theorem		⊢
	proveit.logic.equality.sub_right_side_into
85	instantiation	95, 141, 152, 96	⊢
	: , : , :
86	instantiation	118, 141, 97	⊢
	: , :
87	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
88	instantiation	98, 99, 100, 101	⊢
	: , : , : , :
89	instantiation	102, 103, 104, 105, 141, 106	⊢
	: , :
90	theorem		⊢
	proveit.numbers.addition.disassociation
91	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
92	instantiation	107	⊢
	: , :
93	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
94	axiom		⊢
	proveit.logic.equality.equals_reflexivity
95	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add_reversed
96	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
97	instantiation	179, 161, 108	⊢
	: , : , :
98	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
99	instantiation	112, 109	⊢
	: , : , :
100	instantiation	110, 111	⊢
	: , :
101	instantiation	112, 113	⊢
	: , : , :
102	theorem		⊢
	proveit.numbers.addition.add_complex_closure
103	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
104	instantiation	114	⊢
	: , : , :
105	instantiation	129, 115	⊢
	:
106	instantiation	129, 116	⊢
	:
107	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
108	instantiation	179, 168, 117	⊢
	: , : , :
109	instantiation	118, 136, 119	⊢
	: , :
110	theorem		⊢
	proveit.logic.equality.equals_reversal
111	instantiation	120, 152, 121, 145, 143	⊢
	: , : , :
112	axiom		⊢
	proveit.logic.equality.substitution
113	instantiation	122, 123, 124	⊢
	: , :
114	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
115	instantiation	125, 126, 127	⊢
	: , :
116	instantiation	179, 161, 128	⊢
	: , : , :
117	instantiation	179, 174, 172	⊢
	: , : , :
118	theorem		⊢
	proveit.numbers.addition.commutation
119	instantiation	129, 141	⊢
	:
120	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
121	instantiation	130, 149	⊢
	:
122	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
123	instantiation	179, 131, 132	⊢
	: , : , :
124	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
125	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
126	instantiation	133, 141, 134, 135	⊢
	: , :
127	instantiation	140, 152, 136	⊢
	: , :
128	instantiation	179, 168, 137	⊢
	: , : , :
129	theorem		⊢
	proveit.numbers.negation.complex_closure
130	theorem		⊢
	proveit.numbers.negation.real_closure
131	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
132	instantiation	179, 138, 139	⊢
	: , : , :
133	theorem		⊢
	proveit.numbers.division.div_complex_closure
134	instantiation	140, 152, 141	⊢
	: , :
135	instantiation	142, 143, 144	⊢
	: , : , :
136	instantiation	179, 161, 145	⊢
	: , : , :
137	instantiation	179, 174, 146	⊢
	: , : , :
138	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
139	instantiation	179, 147, 148	⊢
	: , : , :
140	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
141	instantiation	179, 161, 149	⊢
	: , : , :
142	theorem		⊢
	proveit.logic.equality.sub_left_side_into
143	instantiation	150, 159	⊢
	:
144	instantiation	151, 152	⊢
	:
145	instantiation	153, 154, 155	⊢
	: , : , :
146	instantiation	179, 156, 157	⊢
	: , : , :
147	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
148	instantiation	179, 158, 159	⊢
	: , : , :
149	instantiation	179, 168, 160	⊢
	: , : , :
150	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
151	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
152	instantiation	179, 161, 162	⊢
	: , : , :
153	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
154	instantiation	163, 164	⊢
	: , :
155	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
156	instantiation	165, 167, 166	⊢
	: , :
157	assumption		⊢
158	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
159	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
160	instantiation	179, 174, 167	⊢
	: , : , :
161	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
162	instantiation	179, 168, 169	⊢
	: , : , :
163	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
164	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
165	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
166	instantiation	170, 171, 172	⊢
	: , :
167	instantiation	179, 180, 173	⊢
	: , : , :
168	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
169	instantiation	179, 174, 178	⊢
	: , : , :
170	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
171	instantiation	179, 175, 176	⊢
	: , : , :
172	instantiation	177, 178	⊢
	:
173	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
174	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
175	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
176	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
177	theorem		⊢
	proveit.numbers.negation.int_closure
178	instantiation	179, 180, 181	⊢
	: , : , :
179	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
180	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
181	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements