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