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	⊢
	: , :
1	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_all
2	reference	111	⊢
3	instantiation	122	⊢
	: , : , :
4	instantiation	7, 8, 9	⊢
	: , :
5	instantiation	10, 11, 137, 12, 13, 14*, 15*	⊢
	: , : , :
6	instantiation	16, 17	⊢
	: , :
7	theorem		⊢
	proveit.numbers.ordering.relax_equal_to_less_eq
8	instantiation	194, 181, 18	⊢
	: , : , :
9	instantiation	101	⊢
	:
10	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
11	instantiation	19, 111, 20, 21, 164, 94	⊢
	: , :
12	instantiation	194, 181, 22	⊢
	: , : , :
13	instantiation	23, 180, 179, 170	⊢
	: , : , :
14	instantiation	106, 24, 25, 26	⊢
	: , : , : , :
15	instantiation	118, 27	⊢
	: , :
16	theorem		⊢
	proveit.numbers.ordering.relax_less
17	instantiation	28, 29, 30	⊢
	: , : , :
18	instantiation	194, 189, 31	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.addition.add_real_closure
20	instantiation	122	⊢
	: , : , :
21	instantiation	194, 181, 32	⊢
	: , : , :
22	instantiation	194, 189, 179	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
24	instantiation	83, 33, 34	⊢
	: , : , :
25	instantiation	101	⊢
	:
26	instantiation	118, 35	⊢
	: , :
27	instantiation	106, 36, 37, 38	⊢
	: , : , : , :
28	axiom		⊢
	proveit.numbers.ordering.transitivity_less_less
29	instantiation	39, 40	⊢
	:
30	instantiation	41, 191	⊢
	:
31	instantiation	185, 42, 180	⊢
	: , :
32	instantiation	194, 189, 42	⊢
	: , : , :
33	instantiation	120, 69	⊢
	: , : , :
34	instantiation	83, 43, 44	⊢
	: , : , :
35	instantiation	120, 82	⊢
	: , : , :
36	instantiation	45, 125, 153	⊢
	: , :
37	instantiation	118, 46	⊢
	: , :
38	instantiation	118, 47	⊢
	: , :
39	theorem		⊢
	proveit.numbers.number_sets.integers.negative_if_in_neg_int
40	instantiation	48, 49	⊢
	:
41	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
42	instantiation	192, 186	⊢
	:
43	instantiation	97, 188, 111, 98, 112, 100, 125, 113, 153, 114	⊢
	: , : , : , : , : , :
44	instantiation	86, 98, 196, 100, 50, 125, 113, 153, 80	⊢
	: , : , : , : , : , : , : , :
45	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
46	instantiation	51, 67, 125, 129, 52	⊢
	: , : , :
47	instantiation	83, 53, 54	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.negation.int_neg_closure
49	instantiation	55, 56, 133	⊢
	: , :
50	instantiation	115	⊢
	: , :
51	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
52	instantiation	89, 57, 58	⊢
	: , : , :
53	instantiation	83, 59, 60	⊢
	: , : , :
54	instantiation	83, 61, 62	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
56	instantiation	63, 158, 64	⊢
	:
57	instantiation	83, 65, 66	⊢
	: , : , :
58	instantiation	127, 125, 67	⊢
	: , :
59	instantiation	120, 68	⊢
	: , : , :
60	instantiation	120, 69	⊢
	: , : , :
61	instantiation	83, 70, 71	⊢
	: , : , :
62	instantiation	72, 98, 196, 188, 100, 73, 104, 153, 114, 74*	⊢
	: , : , : , : , : , :
63	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
64	instantiation	75, 76, 77	⊢
	: , : , :
65	instantiation	97, 188, 196, 98, 78, 100, 125, 114, 129	⊢
	: , : , : , : , : , :
66	instantiation	79, 125, 129, 80	⊢
	: , : , :
67	instantiation	194, 174, 81	⊢
	: , : , :
68	instantiation	120, 95	⊢
	: , : , :
69	instantiation	120, 82	⊢
	: , : , :
70	instantiation	83, 84, 85	⊢
	: , : , :
71	instantiation	86, 98, 188, 196, 100, 87, 123, 104, 153, 114, 88	⊢
	: , : , : , : , : , : , : , :
72	theorem		⊢
	proveit.numbers.addition.association
73	instantiation	115	⊢
	: , :
74	instantiation	89, 90, 91	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
76	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
77	instantiation	92, 180, 179, 170	⊢
	: , : , :
78	instantiation	115	⊢
	: , :
79	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_12
80	instantiation	101	⊢
	:
81	instantiation	93, 94, 139	⊢
	: , :
82	instantiation	120, 95	⊢
	: , : , :
83	axiom		⊢
	proveit.logic.equality.equals_transitivity
84	instantiation	97, 98, 196, 188, 100, 99, 123, 104, 96	⊢
	: , : , : , : , : , :
85	instantiation	97, 196, 111, 98, 99, 112, 100, 123, 104, 113, 153, 114	⊢
	: , : , : , : , : , :
86	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general
87	instantiation	115	⊢
	: , :
88	instantiation	101	⊢
	:
89	theorem		⊢
	proveit.logic.equality.sub_right_side_into
90	instantiation	102, 153, 167, 103	⊢
	: , : , :
91	instantiation	127, 153, 104	⊢
	: , :
92	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
93	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
94	instantiation	105, 137	⊢
	:
95	instantiation	106, 107, 108, 109	⊢
	: , : , : , :
96	instantiation	110, 111, 112, 113, 153, 114	⊢
	: , :
97	theorem		⊢
	proveit.numbers.addition.disassociation
98	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
99	instantiation	115	⊢
	: , :
100	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
101	axiom		⊢
	proveit.logic.equality.equals_reflexivity
102	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add_reversed
103	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
104	instantiation	194, 174, 116	⊢
	: , : , :
105	theorem		⊢
	proveit.numbers.negation.real_closure
106	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
107	instantiation	120, 117	⊢
	: , : , :
108	instantiation	118, 119	⊢
	: , :
109	instantiation	120, 121	⊢
	: , : , :
110	theorem		⊢
	proveit.numbers.addition.add_complex_closure
111	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
112	instantiation	122	⊢
	: , : , :
113	instantiation	124, 123	⊢
	:
114	instantiation	124, 125	⊢
	:
115	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
116	instantiation	194, 181, 126	⊢
	: , : , :
117	instantiation	127, 128, 129	⊢
	: , :
118	theorem		⊢
	proveit.logic.equality.equals_reversal
119	instantiation	130, 167, 139, 138, 155	⊢
	: , : , :
120	axiom		⊢
	proveit.logic.equality.substitution
121	instantiation	131, 132, 133	⊢
	: , :
122	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
123	instantiation	134, 135, 136	⊢
	: , :
124	theorem		⊢
	proveit.numbers.negation.complex_closure
125	instantiation	194, 174, 137	⊢
	: , : , :
126	instantiation	194, 189, 187	⊢
	: , : , :
127	theorem		⊢
	proveit.numbers.addition.commutation
128	instantiation	194, 174, 138	⊢
	: , : , :
129	instantiation	194, 174, 139	⊢
	: , : , :
130	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
131	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
132	instantiation	194, 140, 141	⊢
	: , : , :
133	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
134	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
135	instantiation	142, 153, 143, 144	⊢
	: , :
136	instantiation	194, 174, 145	⊢
	: , : , :
137	instantiation	194, 181, 146	⊢
	: , : , :
138	instantiation	147, 148, 184	⊢
	: , : , :
139	instantiation	194, 181, 149	⊢
	: , : , :
140	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
141	instantiation	194, 150, 151	⊢
	: , : , :
142	theorem		⊢
	proveit.numbers.division.div_complex_closure
143	instantiation	152, 167, 153	⊢
	: , :
144	instantiation	154, 155, 156	⊢
	: , : , :
145	instantiation	194, 181, 157	⊢
	: , : , :
146	instantiation	194, 189, 158	⊢
	: , : , :
147	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
148	instantiation	159, 160	⊢
	: , :
149	instantiation	194, 189, 161	⊢
	: , : , :
150	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
151	instantiation	194, 162, 163	⊢
	: , : , :
152	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
153	instantiation	194, 174, 164	⊢
	: , : , :
154	theorem		⊢
	proveit.logic.equality.sub_left_side_into
155	instantiation	165, 172	⊢
	:
156	instantiation	166, 167	⊢
	:
157	instantiation	194, 189, 168	⊢
	: , : , :
158	instantiation	194, 169, 170	⊢
	: , : , :
159	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
160	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
161	instantiation	192, 180	⊢
	:
162	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
163	instantiation	194, 171, 172	⊢
	: , : , :
164	instantiation	194, 181, 173	⊢
	: , : , :
165	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
166	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
167	instantiation	194, 174, 175	⊢
	: , : , :
168	instantiation	176, 193, 177	⊢
	: , :
169	instantiation	178, 180, 179	⊢
	: , :
170	assumption		⊢
171	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
172	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
173	instantiation	194, 189, 180	⊢
	: , : , :
174	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
175	instantiation	194, 181, 182	⊢
	: , : , :
176	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
177	instantiation	194, 183, 184	⊢
	: , : , :
178	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
179	instantiation	185, 186, 187	⊢
	: , :
180	instantiation	194, 195, 188	⊢
	: , : , :
181	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
182	instantiation	194, 189, 193	⊢
	: , : , :
183	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
184	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
185	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
186	instantiation	194, 190, 191	⊢
	: , : , :
187	instantiation	192, 193	⊢
	:
188	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
189	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
190	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
191	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
192	theorem		⊢
	proveit.numbers.negation.int_closure
193	instantiation	194, 195, 196	⊢
	: , : , :
194	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
195	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
196	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements