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