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*	,  ⊢
	: , : , : , :
1	theorem		⊢
	proveit.numbers.division.prod_of_fracs
2	reference	38	⊢
3	reference	11	⊢
4	instantiation	215, 173, 8	⊢
	: , : , :
5	instantiation	9, 159, 10	,  ⊢
	: , :
6	instantiation	196, 11	⊢
	:
7	instantiation	166, 12, 13	,  ⊢
	: , : , :
8	instantiation	215, 191, 14	⊢
	: , : , :
9	theorem		⊢
	proveit.numbers.multiplication.mult_complex_nonzero_closure_bin
10	instantiation	15, 21, 16	,  ⊢
	:
11	instantiation	215, 205, 17	⊢
	: , : , :
12	instantiation	78, 210, 217, 112, 18, 113, 20, 198, 21	,  ⊢
	: , : , : , : , : , :
13	instantiation	19, 112, 210, 113, 20, 198, 21	,  ⊢
	: , : , : , : , : , : , :
14	instantiation	215, 202, 22	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
16	instantiation	23, 24	,  ⊢
	: , :
17	instantiation	215, 25, 26	⊢
	: , : , :
18	instantiation	195	⊢
	: , :
19	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
20	instantiation	215, 205, 27	⊢
	: , : , :
21	instantiation	215, 205, 29	,  ⊢
	: , : , :
22	instantiation	215, 208, 35	⊢
	: , : , :
23	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
24	instantiation	28, 118, 29, 30	,  ⊢
	: , :
25	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_nonneg_within_real
26	instantiation	31, 32	⊢
	:
27	instantiation	33, 34, 35	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq
29	instantiation	52, 118, 179, 36	,  ⊢
	: , : , :
30	instantiation	60, 118, 179, 36	,  ⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.absolute_value.abs_complex_closure
32	instantiation	37, 38, 39	⊢
	: , :
33	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
34	instantiation	40, 41	⊢
	: , :
35	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
36	instantiation	42, 43	,  ⊢
	:
37	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
38	instantiation	215, 205, 179	⊢
	: , : , :
39	instantiation	44, 45	⊢
	:
40	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
41	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
42	theorem		⊢
	proveit.trigonometry.sine_pos_interval
43	instantiation	46, 118, 161, 47, 48	,  ⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.negation.complex_closure
45	instantiation	49, 50, 51	⊢
	: , :
46	theorem		⊢
	proveit.numbers.number_sets.real_numbers.in_IntervalOO
47	instantiation	52, 118, 71, 69	,  ⊢
	: , : , :
48	instantiation	53, 54, 55	,  ⊢
	: , :
49	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
50	instantiation	215, 205, 56	⊢
	: , : , :
51	instantiation	57, 58, 59	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
53	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
54	instantiation	60, 118, 71, 69	,  ⊢
	: , : , :
55	instantiation	61, 62, 63	,  ⊢
	: , : , :
56	instantiation	215, 176, 64	⊢
	: , : , :
57	theorem		⊢
	proveit.logic.equality.sub_right_side_into
58	instantiation	76, 77, 65	⊢
	: , :
59	instantiation	166, 66, 67	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
61	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less
62	instantiation	68, 118, 71, 69	,  ⊢
	: , : , :
63	instantiation	70, 71, 72, 124, 73, 74*, 75*	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
65	instantiation	76, 81, 82	⊢
	: , :
66	instantiation	78, 210, 217, 112, 80, 113, 77, 81, 82	⊢
	: , : , : , : , : , :
67	instantiation	78, 112, 217, 113, 79, 80, 198, 145, 81, 82	⊢
	: , : , : , : , : , :
68	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_upper_bound
69	instantiation	83, 141, 84	,  ⊢
	:
70	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
71	instantiation	178, 161, 206, 180	⊢
	: , :
72	instantiation	130, 131, 118	⊢
	: , :
73	instantiation	85, 131, 118, 161, 86, 87	⊢
	: , : , :
74	instantiation	88, 89, 90, 91	⊢
	: , : , : , :
75	instantiation	166, 92, 93	⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
77	instantiation	215, 205, 94	⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.multiplication.disassociation
79	instantiation	195	⊢
	: , :
80	instantiation	195	⊢
	: , :
81	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
82	instantiation	215, 205, 95	⊢
	: , : , :
83	theorem		⊢
	proveit.physics.quantum.QPE._scaled_abs_delta_b_floor_diff_interval
84	assumption		⊢
85	theorem		⊢
	proveit.numbers.multiplication.strong_bound_via_right_factor_bound
86	instantiation	96, 177	⊢
	:
87	instantiation	97, 148	⊢
	:
88	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
89	instantiation	166, 98, 99	⊢
	: , : , :
90	instantiation	100	⊢
	:
91	instantiation	101, 123	⊢
	: , :
92	instantiation	142, 123	⊢
	: , : , :
93	instantiation	101, 102, 103*	⊢
	: , :
94	instantiation	130, 206, 161	⊢
	: , :
95	instantiation	104, 105, 106	⊢
	: , :
96	theorem		⊢
	proveit.numbers.number_sets.real_numbers.positive_if_in_real_pos
97	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
98	instantiation	166, 107, 108	⊢
	: , : , :
99	instantiation	109, 110	⊢
	:
100	axiom		⊢
	proveit.logic.equality.equals_reflexivity
101	theorem		⊢
	proveit.logic.equality.equals_reversal
102	instantiation	111, 112, 217, 210, 113, 114, 146, 145	⊢
	: , : , : , : , : , :
103	instantiation	166, 115, 116	⊢
	: , : , :
104	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
105	instantiation	117, 118, 179, 119	⊢
	: , : , :
106	instantiation	120, 121	⊢
	:
107	instantiation	142, 122	⊢
	: , : , :
108	instantiation	142, 123	⊢
	: , : , :
109	theorem		⊢
	proveit.numbers.addition.elim_zero_left
110	instantiation	215, 205, 124	⊢
	: , : , :
111	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
112	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
113	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
114	instantiation	195	⊢
	: , :
115	instantiation	142, 125	⊢
	: , : , :
116	instantiation	196, 145	⊢
	:
117	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
118	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
119	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval
120	theorem		⊢
	proveit.numbers.negation.real_closure
121	instantiation	215, 211, 126	⊢
	: , : , :
122	instantiation	127, 146	⊢
	:
123	instantiation	128, 145, 198, 180, 129*	⊢
	: , :
124	instantiation	130, 131, 161	⊢
	: , :
125	instantiation	132, 204, 214, 133*	⊢
	: , : , : , :
126	instantiation	215, 213, 134	⊢
	: , : , :
127	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
128	theorem		⊢
	proveit.numbers.division.div_as_mult
129	instantiation	166, 135, 136	⊢
	: , : , :
130	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
131	instantiation	215, 211, 137	⊢
	: , : , :
132	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
133	instantiation	166, 138, 139	⊢
	: , : , :
134	instantiation	215, 140, 141	⊢
	: , : , :
135	instantiation	142, 143	⊢
	: , : , :
136	instantiation	144, 145, 146	⊢
	: , :
137	instantiation	215, 147, 148	⊢
	: , : , :
138	instantiation	183, 217, 149, 150, 151, 152	⊢
	: , : , : , :
139	instantiation	153, 154, 155	⊢
	:
140	instantiation	156, 157, 190	⊢
	: , :
141	assumption		⊢
142	axiom		⊢
	proveit.logic.equality.substitution
143	instantiation	158, 159, 181, 160*	⊢
	: , :
144	theorem		⊢
	proveit.numbers.multiplication.commutation
145	instantiation	215, 205, 161	⊢
	: , : , :
146	instantiation	215, 205, 162	⊢
	: , : , :
147	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
148	instantiation	163, 164, 165	⊢
	: , :
149	instantiation	195	⊢
	: , :
150	instantiation	195	⊢
	: , :
151	instantiation	166, 167, 168	⊢
	: , : , :
152	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
153	theorem		⊢
	proveit.numbers.division.frac_cancel_complete
154	instantiation	215, 205, 169	⊢
	: , : , :
155	instantiation	194, 170	⊢
	:
156	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
157	instantiation	171, 172, 204	⊢
	: , :
158	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
159	instantiation	215, 173, 174	⊢
	: , : , :
160	instantiation	175, 198	⊢
	:
161	instantiation	215, 176, 177	⊢
	: , : , :
162	instantiation	178, 179, 206, 180	⊢
	: , :
163	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
164	instantiation	215, 182, 181	⊢
	: , : , :
165	instantiation	215, 182, 209	⊢
	: , : , :
166	axiom		⊢
	proveit.logic.equality.equals_transitivity
167	instantiation	183, 217, 184, 185, 186, 187	⊢
	: , : , : , :
168	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
169	instantiation	215, 211, 188	⊢
	: , : , :
170	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
171	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
172	instantiation	189, 190	⊢
	:
173	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
174	instantiation	215, 191, 192	⊢
	: , : , :
175	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
176	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
177	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
178	theorem		⊢
	proveit.numbers.division.div_real_closure
179	instantiation	215, 211, 193	⊢
	: , : , :
180	instantiation	194, 209	⊢
	:
181	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
182	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
183	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
184	instantiation	195	⊢
	: , :
185	instantiation	195	⊢
	: , :
186	instantiation	196, 198	⊢
	:
187	instantiation	197, 198	⊢
	:
188	instantiation	215, 213, 199	⊢
	: , : , :
189	theorem		⊢
	proveit.numbers.negation.int_closure
190	instantiation	215, 200, 201	⊢
	: , : , :
191	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
192	instantiation	215, 202, 203	⊢
	: , : , :
193	instantiation	215, 213, 204	⊢
	: , : , :
194	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
195	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
196	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
197	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
198	instantiation	215, 205, 206	⊢
	: , : , :
199	instantiation	215, 216, 207	⊢
	: , : , :
200	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
201	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
202	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
203	instantiation	215, 208, 209	⊢
	: , : , :
204	instantiation	215, 216, 210	⊢
	: , : , :
205	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
206	instantiation	215, 211, 212	⊢
	: , : , :
207	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
208	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
209	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
210	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
211	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
212	instantiation	215, 213, 214	⊢
	: , : , :
213	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
214	instantiation	215, 216, 217	⊢
	: , : , :
215	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
216	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
217	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements