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