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