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	instantiation	91, 68, 163	⊢
	: , :
3	instantiation	91, 61, 163	⊢
	: , :
4	reference	92	⊢
5	instantiation	6, 7, 8, 9, 10, 11	⊢
	: , :
6	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_all
7	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
8	instantiation	12	⊢
	: , : , :
9	instantiation	13, 14, 15	⊢
	: , : , :
10	instantiation	21, 136, 30, 16, 17, 18*	⊢
	: , : , :
11	instantiation	19, 22, 20	⊢
	: , :
12	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
13	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less_eq
14	instantiation	21, 48, 136, 22, 23, 24*, 25*	⊢
	: , : , :
15	instantiation	26, 27	⊢
	: , :
16	instantiation	28, 31, 136	⊢
	: , :
17	instantiation	29, 30, 31, 136, 32, 33	⊢
	: , : , :
18	instantiation	93, 34, 52, 35	⊢
	: , : , : , :
19	theorem		⊢
	proveit.numbers.ordering.relax_equal_to_less_eq
20	instantiation	77	⊢
	:
21	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
22	instantiation	142, 143, 105	⊢
	: , : , :
23	instantiation	36, 105	⊢
	:
24	instantiation	118, 126, 37	⊢
	: , :
25	instantiation	74, 38, 39	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.ordering.relax_less
27	instantiation	40, 41	⊢
	:
28	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
29	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right
30	instantiation	169, 158, 42	⊢
	: , : , :
31	instantiation	169, 158, 43	⊢
	: , : , :
32	instantiation	44, 163, 80, 81	⊢
	: , : , :
33	instantiation	45, 168	⊢
	:
34	instantiation	74, 46, 47	⊢
	: , : , :
35	instantiation	107, 82	⊢
	: , :
36	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
37	instantiation	169, 148, 48	⊢
	: , : , :
38	instantiation	74, 49, 50	⊢
	: , : , :
39	instantiation	51, 89, 52	⊢
	: , :
40	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
41	instantiation	53, 54, 124	⊢
	: , :
42	instantiation	169, 166, 61	⊢
	: , : , :
43	instantiation	169, 166, 80	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
45	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
46	instantiation	109, 55	⊢
	: , : , :
47	instantiation	74, 56, 57	⊢
	: , : , :
48	instantiation	169, 158, 58	⊢
	: , : , :
49	instantiation	109, 82	⊢
	: , : , :
50	instantiation	109, 59	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
52	instantiation	77	⊢
	:
53	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
54	instantiation	60, 61, 62	⊢
	:
55	instantiation	74, 63, 64	⊢
	: , : , :
56	instantiation	83, 86, 171, 168, 88, 65, 89, 120, 126	⊢
	: , : , : , : , : , :
57	instantiation	66, 126, 89, 67	⊢
	: , : , :
58	instantiation	169, 166, 68	⊢
	: , : , :
59	instantiation	109, 82	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
61	instantiation	169, 69, 81	⊢
	: , : , :
62	instantiation	70, 71, 72	⊢
	: , : , :
63	instantiation	109, 73	⊢
	: , : , :
64	instantiation	74, 75, 76	⊢
	: , : , :
65	instantiation	97	⊢
	: , :
66	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
67	instantiation	77	⊢
	:
68	instantiation	162, 92	⊢
	:
69	instantiation	78, 163, 80	⊢
	: , :
70	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
71	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
72	instantiation	79, 163, 80, 81	⊢
	: , : , :
73	instantiation	109, 82	⊢
	: , : , :
74	axiom		⊢
	proveit.logic.equality.equals_transitivity
75	instantiation	83, 86, 171, 168, 88, 84, 89, 117, 126	⊢
	: , : , : , : , : , :
76	instantiation	85, 168, 171, 86, 87, 88, 89, 117, 126, 90*	⊢
	: , : , : , : , : , :
77	axiom		⊢
	proveit.logic.equality.equals_reflexivity
78	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
79	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
80	instantiation	91, 92, 152	⊢
	: , :
81	assumption		⊢
82	instantiation	93, 94, 95, 96	⊢
	: , : , : , :
83	theorem		⊢
	proveit.numbers.addition.disassociation
84	instantiation	97	⊢
	: , :
85	theorem		⊢
	proveit.numbers.addition.association
86	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
87	instantiation	97	⊢
	: , :
88	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
89	instantiation	98, 99, 100	⊢
	: , :
90	instantiation	101, 102, 103	⊢
	: , : , :
91	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
92	instantiation	169, 104, 105	⊢
	: , : , :
93	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
94	instantiation	109, 106	⊢
	: , : , :
95	instantiation	107, 108	⊢
	: , :
96	instantiation	109, 110	⊢
	: , : , :
97	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
98	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
99	instantiation	111, 126, 112, 113	⊢
	: , :
100	instantiation	169, 148, 114	⊢
	: , : , :
101	theorem		⊢
	proveit.logic.equality.sub_right_side_into
102	instantiation	115, 126, 139, 116	⊢
	: , : , :
103	instantiation	118, 126, 117	⊢
	: , :
104	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
105	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
106	instantiation	118, 119, 120	⊢
	: , :
107	theorem		⊢
	proveit.logic.equality.equals_reversal
108	instantiation	121, 139, 133, 132, 128	⊢
	: , : , :
109	axiom		⊢
	proveit.logic.equality.substitution
110	instantiation	122, 123, 124	⊢
	: , :
111	theorem		⊢
	proveit.numbers.division.div_complex_closure
112	instantiation	125, 139, 126	⊢
	: , :
113	instantiation	127, 128, 129	⊢
	: , : , :
114	instantiation	169, 158, 130	⊢
	: , : , :
115	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add_reversed
116	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
117	instantiation	169, 148, 131	⊢
	: , : , :
118	theorem		⊢
	proveit.numbers.addition.commutation
119	instantiation	169, 148, 132	⊢
	: , : , :
120	instantiation	169, 148, 133	⊢
	: , : , :
121	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
122	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
123	instantiation	169, 134, 135	⊢
	: , : , :
124	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
125	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
126	instantiation	169, 148, 136	⊢
	: , : , :
127	theorem		⊢
	proveit.logic.equality.sub_left_side_into
128	instantiation	137, 165	⊢
	:
129	instantiation	138, 139	⊢
	:
130	instantiation	169, 166, 140	⊢
	: , : , :
131	instantiation	169, 158, 141	⊢
	: , : , :
132	instantiation	142, 143, 161	⊢
	: , : , :
133	instantiation	169, 158, 144	⊢
	: , : , :
134	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
135	instantiation	169, 145, 146	⊢
	: , : , :
136	instantiation	169, 158, 147	⊢
	: , : , :
137	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
138	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
139	instantiation	169, 148, 149	⊢
	: , : , :
140	instantiation	150, 167, 151	⊢
	: , :
141	instantiation	169, 166, 152	⊢
	: , : , :
142	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
143	instantiation	153, 154	⊢
	: , :
144	instantiation	169, 166, 155	⊢
	: , : , :
145	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
146	instantiation	169, 156, 157	⊢
	: , : , :
147	instantiation	169, 166, 163	⊢
	: , : , :
148	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
149	instantiation	169, 158, 159	⊢
	: , : , :
150	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
151	instantiation	169, 160, 161	⊢
	: , : , :
152	instantiation	162, 167	⊢
	:
153	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
154	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
155	instantiation	162, 163	⊢
	:
156	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
157	instantiation	169, 164, 165	⊢
	: , : , :
158	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
159	instantiation	169, 166, 167	⊢
	: , : , :
160	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
161	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
162	theorem		⊢
	proveit.numbers.negation.int_closure
163	instantiation	169, 170, 168	⊢
	: , : , :
164	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
165	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
166	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
167	instantiation	169, 170, 171	⊢
	: , : , :
168	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
169	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
170	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
171	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements