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	⊢
	: , : , : , :
1	reference	98	⊢
2	instantiation	32, 5, 6, 7, 8*	⊢
	: , :
3	instantiation	9, 56, 77	⊢
	: , :
4	instantiation	10, 11	⊢
	: , :
5	instantiation	95, 12, 13	⊢
	: , : , :
6	instantiation	203, 181, 25	⊢
	: , : , :
7	instantiation	14, 202, 20, 123, 15	⊢
	: , :
8	instantiation	155, 16, 17	⊢
	: , : , :
9	theorem		⊢
	proveit.numbers.addition.commutation
10	theorem		⊢
	proveit.logic.equality.equals_reversal
11	instantiation	166, 18	⊢
	: , : , :
12	instantiation	203, 181, 19	⊢
	: , : , :
13	instantiation	111, 113, 202, 200, 114, 20, 175, 135, 71	⊢
	: , : , : , : , : , :
14	theorem		⊢
	proveit.numbers.multiplication.mult_not_eq_zero
15	instantiation	203, 140, 107	⊢
	: , : , :
16	instantiation	166, 21	⊢
	: , : , :
17	instantiation	155, 22, 23	⊢
	: , : , :
18	instantiation	166, 24	⊢
	: , : , :
19	instantiation	145, 25, 85	⊢
	: , :
20	instantiation	136	⊢
	: , :
21	instantiation	26, 175, 135, 102, 94, 87, 27*	⊢
	: , : , :
22	instantiation	155, 28, 29	⊢
	: , : , :
23	instantiation	155, 30, 31	⊢
	: , : , :
24	instantiation	32, 116, 33, 34, 35*	⊢
	: , :
25	instantiation	145, 182, 151	⊢
	: , :
26	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_product
27	instantiation	36, 123, 173, 37*	⊢
	: , :
28	instantiation	155, 38, 39	⊢
	: , : , :
29	instantiation	155, 40, 41	⊢
	: , : , :
30	instantiation	112, 113, 62, 114, 64, 135, 71, 70	⊢
	: , : , : , :
31	instantiation	155, 42, 43	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.division.div_as_mult
33	instantiation	203, 181, 44	⊢
	: , : , :
34	instantiation	120, 59	⊢
	:
35	instantiation	45, 175, 92, 102, 94, 46*	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
37	instantiation	108, 175	⊢
	:
38	instantiation	111, 113, 62, 200, 114, 49, 175, 135, 71, 47	⊢
	: , : , : , : , : , :
39	instantiation	111, 62, 202, 113, 49, 48, 114, 175, 135, 71, 65, 70	⊢
	: , : , : , : , : , :
40	instantiation	67, 113, 62, 200, 114, 49, 175, 135, 71, 65, 70	⊢
	: , : , : , : , : , : , :
41	instantiation	155, 50, 51	⊢
	: , : , :
42	instantiation	155, 52, 53	⊢
	: , : , :
43	instantiation	54, 200, 202, 113, 55, 114, 149, 56, 77, 57*, 58*	⊢
	: , : , : , : , : , :
44	instantiation	118, 119, 59	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_real_power
46	instantiation	74, 78, 149, 60*	⊢
	: , :
47	instantiation	61, 65, 70	⊢
	: , :
48	instantiation	136	⊢
	: , :
49	instantiation	79	⊢
	: , : , :
50	instantiation	68, 113, 202, 62, 114, 63, 64, 65, 175, 135, 71, 70	⊢
	: , : , : , : , : , :
51	instantiation	166, 66	⊢
	: , : , :
52	instantiation	67, 200, 113, 114, 135, 71, 70	⊢
	: , : , : , : , : , : , :
53	instantiation	68, 113, 202, 200, 114, 69, 135, 70, 71, 72*	⊢
	: , : , : , : , : , :
54	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
55	instantiation	136	⊢
	: , :
56	instantiation	73, 75	⊢
	:
57	instantiation	74, 149, 75, 76*	⊢
	: , :
58	instantiation	165, 77	⊢
	:
59	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
60	instantiation	174, 78	⊢
	:
61	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
62	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
63	instantiation	136	⊢
	: , :
64	instantiation	79	⊢
	: , : , :
65	instantiation	203, 181, 80	⊢
	: , : , :
66	instantiation	95, 81, 82	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
68	theorem		⊢
	proveit.numbers.multiplication.association
69	instantiation	136	⊢
	: , :
70	instantiation	83, 135, 84	⊢
	: , :
71	instantiation	203, 181, 85	⊢
	: , : , :
72	instantiation	86, 135, 160, 102, 87, 88*, 89*	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.negation.complex_closure
74	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
75	instantiation	203, 181, 129	⊢
	: , : , :
76	instantiation	155, 90, 91	⊢
	: , : , :
77	instantiation	203, 181, 105	⊢
	: , : , :
78	instantiation	203, 181, 92	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
80	instantiation	93, 160, 182, 94	⊢
	: , :
81	instantiation	95, 96, 97	⊢
	: , : , :
82	instantiation	98, 99, 100, 101	⊢
	: , : , : , :
83	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
84	instantiation	203, 181, 102	⊢
	: , : , :
85	instantiation	103, 104, 105	⊢
	: , :
86	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
87	instantiation	106, 107	⊢
	:
88	instantiation	108, 135	⊢
	:
89	instantiation	155, 109, 110	⊢
	: , : , :
90	instantiation	111, 200, 202, 113, 115, 114, 149, 116, 117	⊢
	: , : , : , : , : , :
91	instantiation	112, 113, 202, 114, 115, 116, 117	⊢
	: , : , : , :
92	instantiation	118, 119, 195	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.division.div_real_closure
94	instantiation	120, 194	⊢
	:
95	theorem		⊢
	proveit.logic.equality.sub_right_side_into
96	instantiation	121, 149, 122, 123	⊢
	: , : , : , : , :
97	instantiation	155, 124, 125	⊢
	: , : , :
98	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
99	instantiation	166, 126	⊢
	: , : , :
100	instantiation	166, 126	⊢
	: , : , :
101	instantiation	174, 149	⊢
	:
102	instantiation	203, 188, 127	⊢
	: , : , :
103	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
104	instantiation	128, 129	⊢
	:
105	instantiation	130, 131	⊢
	:
106	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
107	instantiation	203, 132, 163	⊢
	: , : , :
108	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
109	instantiation	166, 133	⊢
	: , : , :
110	instantiation	134, 135	⊢
	:
111	theorem		⊢
	proveit.numbers.multiplication.disassociation
112	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
113	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
114	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
115	instantiation	136	⊢
	: , :
116	instantiation	203, 181, 146	⊢
	: , : , :
117	instantiation	203, 181, 147	⊢
	: , : , :
118	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
119	instantiation	137, 138	⊢
	: , :
120	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
121	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_denom_left
122	instantiation	203, 140, 139	⊢
	: , : , :
123	instantiation	203, 140, 141	⊢
	: , : , :
124	instantiation	166, 142	⊢
	: , : , :
125	instantiation	166, 143	⊢
	: , : , :
126	instantiation	168, 149	⊢
	:
127	instantiation	203, 196, 144	⊢
	: , : , :
128	theorem		⊢
	proveit.numbers.negation.real_closure
129	instantiation	145, 146, 147	⊢
	: , :
130	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
131	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
132	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
133	instantiation	148, 149, 150	⊢
	: , :
134	theorem		⊢
	proveit.numbers.exponentiation.exp_zero_eq_one
135	instantiation	203, 181, 151	⊢
	: , : , :
136	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
137	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
138	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
139	instantiation	203, 153, 152	⊢
	: , : , :
140	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
141	instantiation	203, 153, 179	⊢
	: , : , :
142	instantiation	166, 154	⊢
	: , : , :
143	instantiation	155, 156, 157	⊢
	: , : , :
144	instantiation	198, 192	⊢
	:
145	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
146	instantiation	203, 188, 158	⊢
	: , : , :
147	instantiation	203, 188, 159	⊢
	: , : , :
148	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
149	instantiation	203, 181, 160	⊢
	: , : , :
150	instantiation	161	⊢
	:
151	instantiation	203, 162, 163	⊢
	: , : , :
152	instantiation	203, 185, 164	⊢
	: , : , :
153	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
154	instantiation	165, 175	⊢
	:
155	axiom		⊢
	proveit.logic.equality.equals_transitivity
156	instantiation	166, 167	⊢
	: , : , :
157	instantiation	168, 175	⊢
	:
158	instantiation	203, 196, 169	⊢
	: , : , :
159	instantiation	203, 170, 171	⊢
	: , : , :
160	instantiation	203, 188, 172	⊢
	: , : , :
161	axiom		⊢
	proveit.logic.equality.equals_reflexivity
162	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
163	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
164	instantiation	203, 193, 173	⊢
	: , : , :
165	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
166	axiom		⊢
	proveit.logic.equality.substitution
167	instantiation	174, 175	⊢
	:
168	theorem		⊢
	proveit.numbers.division.frac_one_denom
169	instantiation	203, 176, 177	⊢
	: , : , :
170	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational
171	instantiation	178, 179, 180	⊢
	: , :
172	instantiation	203, 196, 192	⊢
	: , : , :
173	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
174	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
175	instantiation	203, 181, 182	⊢
	: , : , :
176	instantiation	183, 184, 199	⊢
	: , :
177	assumption		⊢
178	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_nonzero_closure
179	instantiation	203, 185, 186	⊢
	: , : , :
180	instantiation	198, 187	⊢
	:
181	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
182	instantiation	203, 188, 189	⊢
	: , : , :
183	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
184	instantiation	190, 191, 192	⊢
	: , :
185	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
186	instantiation	203, 193, 194	⊢
	: , : , :
187	instantiation	203, 204, 195	⊢
	: , : , :
188	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
189	instantiation	203, 196, 197	⊢
	: , : , :
190	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
191	instantiation	198, 199	⊢
	:
192	instantiation	203, 201, 200	⊢
	: , : , :
193	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
194	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
195	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
196	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
197	instantiation	203, 201, 202	⊢
	: , : , :
198	theorem		⊢
	proveit.numbers.negation.int_closure
199	instantiation	203, 204, 205	⊢
	: , : , :
200	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
201	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
202	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
203	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
204	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
205	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
*equality replacement requirements