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	⊢
	: , : , : , :
1	theorem		⊢
	proveit.numbers.number_sets.integers.interval_subset_eq
2	reference	36	⊢
3	instantiation	197, 6	⊢
	:
4	reference	191	⊢
5	instantiation	7, 116, 8, 9, 10, 11	⊢
	: , :
6	instantiation	190, 163, 185	⊢
	: , :
7	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_all
8	instantiation	127	⊢
	: , : , :
9	instantiation	12, 13, 14	⊢
	: , :
10	instantiation	15, 16, 142, 17, 18, 19*, 20*	⊢
	: , : , :
11	instantiation	21, 22	⊢
	: , :
12	theorem		⊢
	proveit.numbers.ordering.relax_equal_to_less_eq
13	instantiation	199, 186, 23	⊢
	: , : , :
14	instantiation	106	⊢
	:
15	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
16	instantiation	24, 116, 25, 26, 169, 99	⊢
	: , :
17	instantiation	199, 186, 27	⊢
	: , : , :
18	instantiation	28, 185, 184, 175	⊢
	: , : , :
19	instantiation	111, 29, 30, 31	⊢
	: , : , : , :
20	instantiation	123, 32	⊢
	: , :
21	theorem		⊢
	proveit.numbers.ordering.relax_less
22	instantiation	33, 34, 35	⊢
	: , : , :
23	instantiation	199, 194, 36	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.addition.add_real_closure
25	instantiation	127	⊢
	: , : , :
26	instantiation	199, 186, 37	⊢
	: , : , :
27	instantiation	199, 194, 184	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
29	instantiation	88, 38, 39	⊢
	: , : , :
30	instantiation	106	⊢
	:
31	instantiation	123, 40	⊢
	: , :
32	instantiation	111, 41, 42, 43	⊢
	: , : , : , :
33	axiom		⊢
	proveit.numbers.ordering.transitivity_less_less
34	instantiation	44, 45	⊢
	:
35	instantiation	46, 196	⊢
	:
36	instantiation	190, 47, 185	⊢
	: , :
37	instantiation	199, 194, 47	⊢
	: , : , :
38	instantiation	125, 74	⊢
	: , : , :
39	instantiation	88, 48, 49	⊢
	: , : , :
40	instantiation	125, 87	⊢
	: , : , :
41	instantiation	50, 130, 158	⊢
	: , :
42	instantiation	123, 51	⊢
	: , :
43	instantiation	123, 52	⊢
	: , :
44	theorem		⊢
	proveit.numbers.number_sets.integers.negative_if_in_neg_int
45	instantiation	53, 54	⊢
	:
46	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
47	instantiation	197, 191	⊢
	:
48	instantiation	102, 193, 116, 103, 117, 105, 130, 118, 158, 119	⊢
	: , : , : , : , : , :
49	instantiation	91, 103, 201, 105, 55, 130, 118, 158, 85	⊢
	: , : , : , : , : , : , : , :
50	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
51	instantiation	56, 72, 130, 134, 57	⊢
	: , : , :
52	instantiation	88, 58, 59	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.negation.int_neg_closure
54	instantiation	60, 61, 138	⊢
	: , :
55	instantiation	120	⊢
	: , :
56	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
57	instantiation	94, 62, 63	⊢
	: , : , :
58	instantiation	88, 64, 65	⊢
	: , : , :
59	instantiation	88, 66, 67	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
61	instantiation	68, 163, 69	⊢
	:
62	instantiation	88, 70, 71	⊢
	: , : , :
63	instantiation	132, 130, 72	⊢
	: , :
64	instantiation	125, 73	⊢
	: , : , :
65	instantiation	125, 74	⊢
	: , : , :
66	instantiation	88, 75, 76	⊢
	: , : , :
67	instantiation	77, 103, 201, 193, 105, 78, 109, 158, 119, 79*	⊢
	: , : , : , : , : , :
68	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
69	instantiation	80, 81, 82	⊢
	: , : , :
70	instantiation	102, 193, 201, 103, 83, 105, 130, 119, 134	⊢
	: , : , : , : , : , :
71	instantiation	84, 130, 134, 85	⊢
	: , : , :
72	instantiation	199, 179, 86	⊢
	: , : , :
73	instantiation	125, 100	⊢
	: , : , :
74	instantiation	125, 87	⊢
	: , : , :
75	instantiation	88, 89, 90	⊢
	: , : , :
76	instantiation	91, 103, 193, 201, 105, 92, 128, 109, 158, 119, 93	⊢
	: , : , : , : , : , : , : , :
77	theorem		⊢
	proveit.numbers.addition.association
78	instantiation	120	⊢
	: , :
79	instantiation	94, 95, 96	⊢
	: , : , :
80	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
81	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
82	instantiation	97, 185, 184, 175	⊢
	: , : , :
83	instantiation	120	⊢
	: , :
84	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_12
85	instantiation	106	⊢
	:
86	instantiation	98, 99, 144	⊢
	: , :
87	instantiation	125, 100	⊢
	: , : , :
88	axiom		⊢
	proveit.logic.equality.equals_transitivity
89	instantiation	102, 103, 201, 193, 105, 104, 128, 109, 101	⊢
	: , : , : , : , : , :
90	instantiation	102, 201, 116, 103, 104, 117, 105, 128, 109, 118, 158, 119	⊢
	: , : , : , : , : , :
91	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general
92	instantiation	120	⊢
	: , :
93	instantiation	106	⊢
	:
94	theorem		⊢
	proveit.logic.equality.sub_right_side_into
95	instantiation	107, 158, 172, 108	⊢
	: , : , :
96	instantiation	132, 158, 109	⊢
	: , :
97	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
98	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
99	instantiation	110, 142	⊢
	:
100	instantiation	111, 112, 113, 114	⊢
	: , : , : , :
101	instantiation	115, 116, 117, 118, 158, 119	⊢
	: , :
102	theorem		⊢
	proveit.numbers.addition.disassociation
103	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
104	instantiation	120	⊢
	: , :
105	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
106	axiom		⊢
	proveit.logic.equality.equals_reflexivity
107	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add_reversed
108	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
109	instantiation	199, 179, 121	⊢
	: , : , :
110	theorem		⊢
	proveit.numbers.negation.real_closure
111	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
112	instantiation	125, 122	⊢
	: , : , :
113	instantiation	123, 124	⊢
	: , :
114	instantiation	125, 126	⊢
	: , : , :
115	theorem		⊢
	proveit.numbers.addition.add_complex_closure
116	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
117	instantiation	127	⊢
	: , : , :
118	instantiation	129, 128	⊢
	:
119	instantiation	129, 130	⊢
	:
120	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
121	instantiation	199, 186, 131	⊢
	: , : , :
122	instantiation	132, 133, 134	⊢
	: , :
123	theorem		⊢
	proveit.logic.equality.equals_reversal
124	instantiation	135, 172, 144, 143, 160	⊢
	: , : , :
125	axiom		⊢
	proveit.logic.equality.substitution
126	instantiation	136, 137, 138	⊢
	: , :
127	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
128	instantiation	139, 140, 141	⊢
	: , :
129	theorem		⊢
	proveit.numbers.negation.complex_closure
130	instantiation	199, 179, 142	⊢
	: , : , :
131	instantiation	199, 194, 192	⊢
	: , : , :
132	theorem		⊢
	proveit.numbers.addition.commutation
133	instantiation	199, 179, 143	⊢
	: , : , :
134	instantiation	199, 179, 144	⊢
	: , : , :
135	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
136	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
137	instantiation	199, 145, 146	⊢
	: , : , :
138	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
139	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
140	instantiation	147, 158, 148, 149	⊢
	: , :
141	instantiation	199, 179, 150	⊢
	: , : , :
142	instantiation	199, 186, 151	⊢
	: , : , :
143	instantiation	152, 153, 189	⊢
	: , : , :
144	instantiation	199, 186, 154	⊢
	: , : , :
145	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
146	instantiation	199, 155, 156	⊢
	: , : , :
147	theorem		⊢
	proveit.numbers.division.div_complex_closure
148	instantiation	157, 172, 158	⊢
	: , :
149	instantiation	159, 160, 161	⊢
	: , : , :
150	instantiation	199, 186, 162	⊢
	: , : , :
151	instantiation	199, 194, 163	⊢
	: , : , :
152	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
153	instantiation	164, 165	⊢
	: , :
154	instantiation	199, 194, 166	⊢
	: , : , :
155	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
156	instantiation	199, 167, 168	⊢
	: , : , :
157	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
158	instantiation	199, 179, 169	⊢
	: , : , :
159	theorem		⊢
	proveit.logic.equality.sub_left_side_into
160	instantiation	170, 177	⊢
	:
161	instantiation	171, 172	⊢
	:
162	instantiation	199, 194, 173	⊢
	: , : , :
163	instantiation	199, 174, 175	⊢
	: , : , :
164	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
165	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
166	instantiation	197, 185	⊢
	:
167	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
168	instantiation	199, 176, 177	⊢
	: , : , :
169	instantiation	199, 186, 178	⊢
	: , : , :
170	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
171	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
172	instantiation	199, 179, 180	⊢
	: , : , :
173	instantiation	181, 198, 182	⊢
	: , :
174	instantiation	183, 185, 184	⊢
	: , :
175	assumption		⊢
176	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
177	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
178	instantiation	199, 194, 185	⊢
	: , : , :
179	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
180	instantiation	199, 186, 187	⊢
	: , : , :
181	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
182	instantiation	199, 188, 189	⊢
	: , : , :
183	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
184	instantiation	190, 191, 192	⊢
	: , :
185	instantiation	199, 200, 193	⊢
	: , : , :
186	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
187	instantiation	199, 194, 198	⊢
	: , : , :
188	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
189	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
190	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
191	instantiation	199, 195, 196	⊢
	: , : , :
192	instantiation	197, 198	⊢
	:
193	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
194	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
195	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
196	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
197	theorem		⊢
	proveit.numbers.negation.int_closure
198	instantiation	199, 200, 201	⊢
	: , : , :
199	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
200	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
201	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements