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	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
2	instantiation	19, 5	⊢
	: , : , :
3	instantiation	19, 6	⊢
	: , : , :
4	instantiation	43, 7	⊢
	: , :
5	instantiation	10, 8, 9	⊢
	: , : , :
6	instantiation	10, 11, 12	⊢
	: , : , :
7	instantiation	13, 167, 177, 120, 14, 121, 31, 15, 16	⊢
	: , : , : , : , : , :
8	instantiation	19, 17	⊢
	: , : , :
9	instantiation	43, 18	⊢
	: , :
10	axiom		⊢
	proveit.logic.equality.equals_transitivity
11	instantiation	19, 20	⊢
	: , : , :
12	instantiation	43, 21	⊢
	: , :
13	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
14	instantiation	22	⊢
	: , :
15	modus ponens	23, 35	⊢
16	modus ponens	24, 39	⊢
17	modus ponens	25, 26	⊢
18	instantiation	27, 121, 31	⊢
	: , :
19	axiom		⊢
	proveit.logic.equality.substitution
20	modus ponens	28, 29	⊢
21	instantiation	30, 121, 31	⊢
	: , :
22	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
23	instantiation	32	⊢
	: , : , :
24	instantiation	32	⊢
	: , : , :
25	instantiation	36, 154	⊢
	: , : , : , : , : , : , :
26	generalization	33	⊢
27	modus ponens	34, 35	⊢
28	instantiation	36, 154	⊢
	: , : , : , : , : , : , :
29	generalization	37	⊢
30	modus ponens	38, 39	⊢
31	instantiation	175, 90, 40	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.summation.summation_complex_closure
33	instantiation	43, 41	,  ⊢
	: , :
34	instantiation	45, 167, 154, 120	⊢
	: , : , : , : , : , :
35	generalization	42	⊢
36	theorem		⊢
	proveit.core_expr_types.lambda_maps.general_lambda_substitution
37	instantiation	43, 44	,  ⊢
	: , :
38	instantiation	45, 167, 154, 120	⊢
	: , : , : , : , : , :
39	generalization	46	⊢
40	instantiation	61, 68, 47, 48	⊢
	: , :
41	instantiation	50, 60, 51, 65, 52*	,  ⊢
	: , : , : , :
42	instantiation	175, 90, 49	,  ⊢
	: , : , :
43	theorem		⊢
	proveit.logic.equality.equals_reversal
44	instantiation	50, 60, 51, 71, 52*	,  ⊢
	: , : , : , :
45	theorem		⊢
	proveit.numbers.multiplication.distribute_through_summation
46	instantiation	175, 90, 53	,  ⊢
	: , : , :
47	instantiation	175, 104, 54	⊢
	: , : , :
48	instantiation	122, 83	⊢
	:
49	instantiation	61, 68, 55, 56	,  ⊢
	: , :
50	theorem		⊢
	proveit.numbers.division.prod_of_fracs
51	instantiation	175, 57, 58	⊢
	: , : , :
52	instantiation	59, 60	⊢
	:
53	instantiation	61, 68, 62, 63	,  ⊢
	: , :
54	instantiation	175, 115, 64	⊢
	: , : , :
55	instantiation	69, 88, 177	,  ⊢
	: , :
56	instantiation	70, 65	,  ⊢
	:
57	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
58	instantiation	175, 66, 67	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
60	instantiation	175, 90, 68	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.division.div_real_closure
62	instantiation	69, 91, 177	,  ⊢
	: , :
63	instantiation	70, 71	,  ⊢
	:
64	instantiation	175, 176, 72	⊢
	: , : , :
65	instantiation	77, 73, 79	,  ⊢
	: , :
66	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
67	instantiation	175, 74, 75	⊢
	: , : , :
68	instantiation	175, 104, 76	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.exponentiation.exp_real_closure_nat_power
70	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_if_in_complex_nonzero
71	instantiation	77, 78, 79	,  ⊢
	: , :
72	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
73	instantiation	84, 80, 81	,  ⊢
	:
74	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
75	instantiation	175, 82, 83	⊢
	: , : , :
76	instantiation	175, 115, 164	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_nonzero_closure
78	instantiation	84, 85, 86	,  ⊢
	:
79	instantiation	175, 90, 87	⊢
	: , : , :
80	instantiation	175, 90, 88	,  ⊢
	: , : , :
81	instantiation	92, 89	,  ⊢
	: , :
82	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
83	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
84	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
85	instantiation	175, 90, 91	,  ⊢
	: , : , :
86	instantiation	92, 93	,  ⊢
	: , :
87	instantiation	175, 104, 94	⊢
	: , : , :
88	instantiation	97, 95, 99	,  ⊢
	: , :
89	instantiation	100, 96	,  ⊢
	: , :
90	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
91	instantiation	97, 98, 99	,  ⊢
	: , :
92	theorem		⊢
	proveit.numbers.addition.subtraction.nonzero_difference_if_different
93	instantiation	100, 101	,  ⊢
	: , :
94	instantiation	175, 115, 174	⊢
	: , : , :
95	instantiation	175, 104, 102	,  ⊢
	: , : , :
96	instantiation	108, 109, 112, 103	,  ⊢
	: , :
97	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
98	instantiation	175, 104, 105	,  ⊢
	: , : , :
99	instantiation	106, 107	⊢
	:
100	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
101	instantiation	108, 109, 133, 110	,  ⊢
	: , :
102	instantiation	175, 115, 112	,  ⊢
	: , : , :
103	instantiation	111, 112, 113, 114	,  ⊢
	: , :
104	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
105	instantiation	175, 115, 133	,  ⊢
	: , : , :
106	theorem		⊢
	proveit.numbers.negation.real_closure
107	instantiation	116, 117, 118	⊢
	: , :
108	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_not_eq_nonzeroInt
109	instantiation	119, 120, 167, 121	⊢
	: , : , : , : , :
110	instantiation	122, 123	,  ⊢
	:
111	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_int
112	instantiation	175, 124, 138	,  ⊢
	: , : , :
113	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
114	instantiation	125, 126, 127	,  ⊢
	: , : , :
115	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
116	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
117	instantiation	128, 129, 130	⊢
	: , : , :
118	instantiation	131, 132	⊢
	:
119	theorem		⊢
	proveit.logic.sets.enumeration.in_enumerated_set
120	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
121	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
122	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
123	instantiation	155, 133, 134	,  ⊢
	:
124	instantiation	162, 136, 137	⊢
	: , :
125	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less
126	instantiation	135, 136, 137, 138	,  ⊢
	: , : , :
127	instantiation	139, 140	⊢
	:
128	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
129	instantiation	141, 142	⊢
	: , :
130	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
131	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
132	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
133	instantiation	175, 143, 151	,  ⊢
	: , : , :
134	instantiation	159, 144, 145	,  ⊢
	: , : , :
135	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
136	instantiation	168, 146, 164	⊢
	: , :
137	instantiation	173, 150	⊢
	:
138	assumption		⊢
139	theorem		⊢
	proveit.numbers.number_sets.integers.negative_if_in_neg_int
140	instantiation	147, 149	⊢
	:
141	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
142	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
143	instantiation	162, 150, 169	⊢
	: , :
144	instantiation	148, 149	⊢
	:
145	instantiation	163, 150, 169, 151	,  ⊢
	: , : , :
146	instantiation	173, 169	⊢
	:
147	theorem		⊢
	proveit.numbers.negation.int_neg_closure
148	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
149	instantiation	152, 153, 154	⊢
	: , :
150	instantiation	168, 156, 164	⊢
	: , :
151	assumption		⊢
152	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
153	instantiation	155, 156, 157	⊢
	:
154	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
155	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
156	instantiation	175, 158, 166	⊢
	: , : , :
157	instantiation	159, 160, 161	⊢
	: , : , :
158	instantiation	162, 164, 165	⊢
	: , :
159	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
160	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
161	instantiation	163, 164, 165, 166	⊢
	: , : , :
162	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
163	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
164	instantiation	175, 176, 167	⊢
	: , : , :
165	instantiation	168, 169, 170	⊢
	: , :
166	assumption		⊢
167	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
168	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
169	instantiation	175, 171, 172	⊢
	: , : , :
170	instantiation	173, 174	⊢
	:
171	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
172	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
173	theorem		⊢
	proveit.numbers.negation.int_closure
174	instantiation	175, 176, 177	⊢
	: , : , :
175	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
176	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
177	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements