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