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	⊢
	: , : , : , :
1	theorem		⊢
	proveit.logic.sets.functions.injections.subset_injection
2	instantiation	4, 125, 5, 154, 6	⊢
	: , : , : , :
3	instantiation	7, 8	⊢
	: , :
4	theorem		⊢
	proveit.numbers.number_sets.integers.interval_subset_eq
5	instantiation	138, 78, 188	⊢
	: , :
6	instantiation	9, 10, 11, 12, 13, 14	⊢
	: , :
7	theorem		⊢
	proveit.logic.booleans.conjunction.left_from_and
8	instantiation	15, 16	⊢
	: , : , :
9	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_all
10	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
11	instantiation	17	⊢
	: , : , :
12	instantiation	18, 19, 20	⊢
	: , : , :
13	instantiation	28, 159, 37, 21, 22, 23*	⊢
	: , : , :
14	instantiation	24, 29, 25	⊢
	: , :
15	theorem		⊢
	proveit.logic.sets.functions.bijections.membership_unfolding
16	instantiation	26, 27	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
18	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less_eq
19	instantiation	28, 62, 159, 29, 30, 31*, 32*	⊢
	: , : , :
20	instantiation	33, 34	⊢
	: , :
21	instantiation	35, 38, 159	⊢
	: , :
22	instantiation	36, 37, 38, 159, 39, 40	⊢
	: , : , :
23	instantiation	113, 41, 66, 42	⊢
	: , : , : , :
24	theorem		⊢
	proveit.numbers.ordering.relax_equal_to_less_eq
25	instantiation	95	⊢
	:
26	theorem		⊢
	proveit.logic.sets.functions.bijections.elim_domain_condition
27	modus ponens	43, 44	⊢
28	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
29	instantiation	167, 168, 166	⊢
	: , : , :
30	instantiation	45, 166	⊢
	:
31	instantiation	140, 148, 46	⊢
	: , :
32	instantiation	92, 47, 48	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.ordering.relax_less
34	instantiation	49, 50	⊢
	:
35	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
36	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right
37	instantiation	194, 183, 51	⊢
	: , : , :
38	instantiation	194, 183, 52	⊢
	: , : , :
39	instantiation	53, 188, 100, 101	⊢
	: , : , :
40	instantiation	54, 193	⊢
	:
41	instantiation	92, 55, 56	⊢
	: , : , :
42	instantiation	127, 102	⊢
	: , :
43	instantiation	57, 58*	⊢
	: , : , : , : , : , :
44	instantiation	59, 60, 61	⊢
	: , :
45	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
46	instantiation	194, 173, 62	⊢
	: , : , :
47	instantiation	92, 63, 64	⊢
	: , : , :
48	instantiation	65, 109, 66	⊢
	: , :
49	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
50	instantiation	67, 68, 146	⊢
	: , :
51	instantiation	194, 191, 78	⊢
	: , : , :
52	instantiation	194, 191, 100	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
54	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
55	instantiation	129, 69	⊢
	: , : , :
56	instantiation	92, 70, 71	⊢
	: , : , :
57	theorem		⊢
	proveit.logic.sets.functions.bijections.bijection_transitivity
58	instantiation	129, 72	⊢
	: , : , :
59	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
60	instantiation	73, 74, 125, 154, 97	⊢
	: , : , : , : , :
61	theorem		⊢
	proveit.physics.quantum.QPE._sample_space_bijection
62	instantiation	194, 183, 75	⊢
	: , : , :
63	instantiation	129, 102	⊢
	: , : , :
64	instantiation	129, 76	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
66	instantiation	95	⊢
	:
67	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
68	instantiation	77, 78, 79	⊢
	:
69	instantiation	92, 80, 81	⊢
	: , : , :
70	instantiation	103, 106, 196, 193, 108, 82, 109, 142, 148	⊢
	: , : , : , : , : , :
71	instantiation	83, 148, 109, 84	⊢
	: , : , :
72	instantiation	127, 85	⊢
	: , :
73	theorem		⊢
	proveit.numbers.modular.interval_left_shift_bijection
74	instantiation	86, 196, 176	⊢
	: , :
75	instantiation	194, 191, 139	⊢
	: , : , :
76	instantiation	129, 102	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
78	instantiation	194, 87, 101	⊢
	: , : , :
79	instantiation	88, 89, 90	⊢
	: , : , :
80	instantiation	129, 91	⊢
	: , : , :
81	instantiation	92, 93, 94	⊢
	: , : , :
82	instantiation	117	⊢
	: , :
83	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
84	instantiation	95	⊢
	:
85	instantiation	96, 97, 98	⊢
	: , :
86	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
87	instantiation	124, 188, 100	⊢
	: , :
88	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
89	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
90	instantiation	99, 188, 100, 101	⊢
	: , : , :
91	instantiation	129, 102	⊢
	: , : , :
92	axiom		⊢
	proveit.logic.equality.equals_transitivity
93	instantiation	103, 106, 196, 193, 108, 104, 109, 137, 148	⊢
	: , : , : , : , : , :
94	instantiation	105, 193, 196, 106, 107, 108, 109, 137, 148, 110*	⊢
	: , : , : , : , : , :
95	axiom		⊢
	proveit.logic.equality.equals_reflexivity
96	axiom		⊢
	proveit.physics.quantum.QPE._mod_add_def
97	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
98	instantiation	194, 111, 112	⊢
	: , : , :
99	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
100	instantiation	138, 154, 177	⊢
	: , :
101	assumption		⊢
102	instantiation	113, 114, 115, 116	⊢
	: , : , : , :
103	theorem		⊢
	proveit.numbers.addition.disassociation
104	instantiation	117	⊢
	: , :
105	theorem		⊢
	proveit.numbers.addition.association
106	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
107	instantiation	117	⊢
	: , :
108	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
109	instantiation	118, 119, 120	⊢
	: , :
110	instantiation	121, 122, 123	⊢
	: , : , :
111	instantiation	124, 125, 154	⊢
	: , :
112	assumption		⊢
113	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
114	instantiation	129, 126	⊢
	: , : , :
115	instantiation	127, 128	⊢
	: , :
116	instantiation	129, 130	⊢
	: , : , :
117	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
118	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
119	instantiation	131, 148, 132, 133	⊢
	: , :
120	instantiation	194, 173, 134	⊢
	: , : , :
121	theorem		⊢
	proveit.logic.equality.sub_right_side_into
122	instantiation	135, 148, 162, 136	⊢
	: , : , :
123	instantiation	140, 148, 137	⊢
	: , :
124	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
125	instantiation	138, 139, 188	⊢
	: , :
126	instantiation	140, 141, 142	⊢
	: , :
127	theorem		⊢
	proveit.logic.equality.equals_reversal
128	instantiation	143, 162, 156, 155, 150	⊢
	: , : , :
129	axiom		⊢
	proveit.logic.equality.substitution
130	instantiation	144, 145, 146	⊢
	: , :
131	theorem		⊢
	proveit.numbers.division.div_complex_closure
132	instantiation	147, 162, 148	⊢
	: , :
133	instantiation	149, 150, 151	⊢
	: , : , :
134	instantiation	194, 183, 152	⊢
	: , : , :
135	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add_reversed
136	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
137	instantiation	194, 173, 153	⊢
	: , : , :
138	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
139	instantiation	187, 154	⊢
	:
140	theorem		⊢
	proveit.numbers.addition.commutation
141	instantiation	194, 173, 155	⊢
	: , : , :
142	instantiation	194, 173, 156	⊢
	: , : , :
143	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
144	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
145	instantiation	194, 157, 158	⊢
	: , : , :
146	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
147	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
148	instantiation	194, 173, 159	⊢
	: , : , :
149	theorem		⊢
	proveit.logic.equality.sub_left_side_into
150	instantiation	160, 190	⊢
	:
151	instantiation	161, 162	⊢
	:
152	instantiation	194, 191, 163	⊢
	: , : , :
153	instantiation	194, 183, 164	⊢
	: , : , :
154	instantiation	194, 165, 166	⊢
	: , : , :
155	instantiation	167, 168, 186	⊢
	: , : , :
156	instantiation	194, 183, 169	⊢
	: , : , :
157	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
158	instantiation	194, 170, 171	⊢
	: , : , :
159	instantiation	194, 183, 172	⊢
	: , : , :
160	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
161	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
162	instantiation	194, 173, 174	⊢
	: , : , :
163	instantiation	175, 192, 176	⊢
	: , :
164	instantiation	194, 191, 177	⊢
	: , : , :
165	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
166	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
167	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
168	instantiation	178, 179	⊢
	: , :
169	instantiation	194, 191, 180	⊢
	: , : , :
170	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
171	instantiation	194, 181, 182	⊢
	: , : , :
172	instantiation	194, 191, 188	⊢
	: , : , :
173	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
174	instantiation	194, 183, 184	⊢
	: , : , :
175	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
176	instantiation	194, 185, 186	⊢
	: , : , :
177	instantiation	187, 192	⊢
	:
178	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
179	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
180	instantiation	187, 188	⊢
	:
181	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
182	instantiation	194, 189, 190	⊢
	: , : , :
183	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
184	instantiation	194, 191, 192	⊢
	: , : , :
185	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
186	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
187	theorem		⊢
	proveit.numbers.negation.int_closure
188	instantiation	194, 195, 193	⊢
	: , : , :
189	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
190	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
191	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
192	instantiation	194, 195, 196	⊢
	: , : , :
193	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
194	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
195	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
196	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements