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, 6, 7*, 8*	⊢
	: , : , : , :
1	theorem		⊢
	proveit.numbers.summation.gen_finite_geom_sum
2	reference	15	⊢
3	instantiation	30, 9, 10	⊢
	: , : , :
4	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
5	instantiation	11, 12, 177	⊢
	: , :
6	instantiation	13, 14	⊢
	: , :
7	instantiation	164, 15	⊢
	:
8	instantiation	192, 16, 17	⊢
	: , : , :
9	instantiation	18, 19, 20, 21*	⊢
	:
10	instantiation	200, 22	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
12	instantiation	217, 23, 83	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.addition.subtraction.nonneg_difference
14	instantiation	24, 83	⊢
	:
15	instantiation	141, 25, 28	⊢
	: , :
16	instantiation	200, 26	⊢
	: , : , :
17	instantiation	27, 49, 28, 53, 29*	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.exponentiation.unit_complex_polar_num_neq_one
19	instantiation	155, 88, 75	⊢
	: , : , :
20	instantiation	30, 31, 32	⊢
	: , : , :
21	instantiation	33, 34	⊢
	: , :
22	instantiation	119, 219, 212, 124, 89, 126, 208, 165, 80, 130	⊢
	: , : , : , : , : , : , :
23	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
24	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
25	instantiation	217, 210, 35	⊢
	: , : , :
26	instantiation	192, 36, 37	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.exponentiation.complex_power_of_complex_power
28	instantiation	155, 38, 39	⊢
	: , : , :
29	instantiation	114, 124, 40, 212, 126, 41, 208, 165, 80, 130, 53	⊢
	: , : , : , : , : , :
30	theorem		⊢
	proveit.logic.equality.sub_left_side_into
31	instantiation	42, 43, 44, 73, 71	⊢
	: , :
32	instantiation	158, 45, 46, 47	⊢
	: , : , : , :
33	theorem		⊢
	proveit.logic.equality.equals_reversal
34	instantiation	200, 48	⊢
	: , : , :
35	instantiation	217, 185, 49	⊢
	: , : , :
36	instantiation	50, 124, 219, 212, 126, 51, 53, 142, 183	⊢
	: , : , : , : , : , :
37	instantiation	52, 183, 53, 175	⊢
	: , : , :
38	instantiation	122, 69, 54	⊢
	: , :
39	instantiation	192, 55, 56	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
41	instantiation	57	⊢
	: , : , : , :
42	theorem		⊢
	proveit.logic.booleans.disjunction.right_if_not_left
43	instantiation	58, 59	⊢
	:
44	instantiation	60, 61	⊢
	: , :
45	instantiation	62, 63, 69, 64, 65*	⊢
	: , :
46	instantiation	199, 130	⊢
	:
47	instantiation	184	⊢
	:
48	instantiation	192, 66, 67	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
50	theorem		⊢
	proveit.numbers.addition.disassociation
51	instantiation	137	⊢
	: , :
52	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
53	instantiation	217, 210, 68	⊢
	: , : , :
54	instantiation	122, 80, 130	⊢
	: , :
55	instantiation	114, 212, 219, 124, 70, 126, 69, 80, 130	⊢
	: , : , : , : , : , :
56	instantiation	114, 124, 219, 126, 89, 70, 208, 165, 80, 130	⊢
	: , : , : , : , : , :
57	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
58	axiom		⊢
	proveit.logic.booleans.negation.operand_is_bool
59	instantiation	72, 71	⊢
	:
60	axiom		⊢
	proveit.logic.booleans.disjunction.right_in_bool
61	instantiation	72, 73	⊢
	:
62	theorem		⊢
	proveit.numbers.division.div_as_mult
63	instantiation	155, 74, 75	⊢
	: , : , :
64	instantiation	76, 219, 89, 170, 77	⊢
	: , :
65	instantiation	192, 78, 79	⊢
	: , : , :
66	instantiation	119, 124, 125, 126, 116, 208, 165, 130, 80	⊢
	: , : , : , : , : , : , :
67	instantiation	123, 212, 125, 124, 116, 126, 80, 208, 165, 130	⊢
	: , : , : , : , : , :
68	instantiation	81, 82, 83	⊢
	: , : , :
69	instantiation	217, 210, 96	⊢
	: , : , :
70	instantiation	137	⊢
	: , :
71	instantiation	84, 85	⊢
	: , :
72	theorem		⊢
	proveit.logic.booleans.in_bool_if_true
73	instantiation	86, 87	⊢
	:
74	instantiation	217, 210, 88	⊢
	: , : , :
75	instantiation	114, 124, 219, 212, 126, 89, 208, 165, 130	⊢
	: , : , : , : , : , :
76	theorem		⊢
	proveit.numbers.multiplication.mult_not_eq_zero
77	instantiation	217, 179, 146	⊢
	: , : , :
78	instantiation	200, 90	⊢
	: , : , :
79	instantiation	192, 91, 92	⊢
	: , : , :
80	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
81	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
82	instantiation	93, 94	⊢
	: , :
83	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
84	theorem		⊢
	proveit.logic.equality.unfold_not_equals
85	assumption		⊢
86	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_zero_or_non_int
87	instantiation	95, 212, 124, 126	⊢
	: , : , : , : , :
88	instantiation	103, 96, 140	⊢
	: , :
89	instantiation	137	⊢
	: , :
90	instantiation	97, 208, 165, 154, 151, 134, 98*	⊢
	: , : , :
91	instantiation	192, 99, 100	⊢
	: , : , :
92	instantiation	192, 101, 102	⊢
	: , : , :
93	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
94	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
95	theorem		⊢
	proveit.logic.sets.enumeration.in_enumerated_set
96	instantiation	103, 211, 176	⊢
	: , :
97	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_product
98	instantiation	104, 170, 204, 105*	⊢
	: , :
99	instantiation	192, 106, 107	⊢
	: , : , :
100	instantiation	192, 108, 109	⊢
	: , : , :
101	instantiation	110, 124, 125, 126, 128, 165, 130, 131	⊢
	: , : , : , :
102	instantiation	192, 111, 112	⊢
	: , : , :
103	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
104	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
105	instantiation	147, 208	⊢
	:
106	instantiation	114, 124, 125, 212, 126, 116, 208, 165, 130, 113	⊢
	: , : , : , : , : , :
107	instantiation	114, 125, 219, 124, 116, 115, 126, 208, 165, 130, 129, 131	⊢
	: , : , : , : , : , :
108	instantiation	119, 124, 125, 212, 126, 116, 208, 165, 130, 129, 131	⊢
	: , : , : , : , : , : , :
109	instantiation	192, 117, 118	⊢
	: , : , :
110	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
111	instantiation	119, 212, 124, 126, 165, 130, 131	⊢
	: , : , : , : , : , : , :
112	instantiation	123, 124, 219, 212, 126, 120, 165, 131, 130, 121*	⊢
	: , : , : , : , : , :
113	instantiation	122, 129, 131	⊢
	: , :
114	theorem		⊢
	proveit.numbers.multiplication.disassociation
115	instantiation	137	⊢
	: , :
116	instantiation	138	⊢
	: , : , :
117	instantiation	123, 124, 219, 125, 126, 127, 128, 129, 208, 165, 130, 131	⊢
	: , : , : , : , : , :
118	instantiation	200, 132	⊢
	: , : , :
119	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
120	instantiation	137	⊢
	: , :
121	instantiation	133, 165, 195, 154, 134, 135*, 136*	⊢
	: , : , :
122	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
123	theorem		⊢
	proveit.numbers.multiplication.association
124	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
125	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
126	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
127	instantiation	137	⊢
	: , :
128	instantiation	138	⊢
	: , : , :
129	instantiation	217, 210, 139	⊢
	: , : , :
130	instantiation	217, 210, 140	⊢
	: , : , :
131	instantiation	141, 165, 142	⊢
	: , :
132	instantiation	155, 143, 144	⊢
	: , : , :
133	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
134	instantiation	145, 146	⊢
	:
135	instantiation	147, 165	⊢
	:
136	instantiation	192, 148, 149	⊢
	: , : , :
137	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
138	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
139	instantiation	150, 195, 211, 151	⊢
	: , :
140	instantiation	152, 153	⊢
	:
141	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
142	instantiation	217, 210, 154	⊢
	: , : , :
143	instantiation	155, 156, 157	⊢
	: , : , :
144	instantiation	158, 159, 160, 161	⊢
	: , : , : , :
145	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
146	instantiation	217, 162, 186	⊢
	: , : , :
147	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
148	instantiation	200, 163	⊢
	: , : , :
149	instantiation	164, 165	⊢
	:
150	theorem		⊢
	proveit.numbers.division.div_real_closure
151	instantiation	166, 206	⊢
	:
152	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
153	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int
154	instantiation	217, 213, 167	⊢
	: , : , :
155	theorem		⊢
	proveit.logic.equality.sub_right_side_into
156	instantiation	168, 183, 169, 170	⊢
	: , : , : , : , :
157	instantiation	192, 171, 172	⊢
	: , : , :
158	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
159	instantiation	200, 173	⊢
	: , : , :
160	instantiation	200, 173	⊢
	: , : , :
161	instantiation	207, 183	⊢
	:
162	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
163	instantiation	174, 183, 175	⊢
	: , :
164	theorem		⊢
	proveit.numbers.exponentiation.exp_zero_eq_one
165	instantiation	217, 210, 176	⊢
	: , : , :
166	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
167	instantiation	217, 215, 177	⊢
	: , : , :
168	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_denom_left
169	instantiation	217, 179, 178	⊢
	: , : , :
170	instantiation	217, 179, 180	⊢
	: , : , :
171	instantiation	200, 181	⊢
	: , : , :
172	instantiation	200, 182	⊢
	: , : , :
173	instantiation	202, 183	⊢
	:
174	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
175	instantiation	184	⊢
	:
176	instantiation	217, 185, 186	⊢
	: , : , :
177	instantiation	187, 209	⊢
	:
178	instantiation	217, 189, 188	⊢
	: , : , :
179	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
180	instantiation	217, 189, 190	⊢
	: , : , :
181	instantiation	200, 191	⊢
	: , : , :
182	instantiation	192, 193, 194	⊢
	: , : , :
183	instantiation	217, 210, 195	⊢
	: , : , :
184	axiom		⊢
	proveit.logic.equality.equals_reflexivity
185	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
186	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
187	theorem		⊢
	proveit.numbers.negation.int_closure
188	instantiation	217, 197, 196	⊢
	: , : , :
189	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
190	instantiation	217, 197, 198	⊢
	: , : , :
191	instantiation	199, 208	⊢
	:
192	axiom		⊢
	proveit.logic.equality.equals_transitivity
193	instantiation	200, 201	⊢
	: , : , :
194	instantiation	202, 208	⊢
	:
195	instantiation	217, 213, 203	⊢
	: , : , :
196	instantiation	217, 205, 204	⊢
	: , : , :
197	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
198	instantiation	217, 205, 206	⊢
	: , : , :
199	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
200	axiom		⊢
	proveit.logic.equality.substitution
201	instantiation	207, 208	⊢
	:
202	theorem		⊢
	proveit.numbers.division.frac_one_denom
203	instantiation	217, 215, 209	⊢
	: , : , :
204	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
205	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
206	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
207	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
208	instantiation	217, 210, 211	⊢
	: , : , :
209	instantiation	217, 218, 212	⊢
	: , : , :
210	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
211	instantiation	217, 213, 214	⊢
	: , : , :
212	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
213	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
214	instantiation	217, 215, 216	⊢
	: , : , :
215	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
216	instantiation	217, 218, 219	⊢
	: , : , :
217	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
218	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
219	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements