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	⊢
	: , :
1	theorem		⊢
	proveit.numbers.ordering.relax_less
2	instantiation	3, 4	⊢
	: , :
3	theorem		⊢
	proveit.numbers.addition.subtraction.pos_difference
4	instantiation	5, 125, 12, 6, 7, 8*, 9*	⊢
	: , : , :
5	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
6	instantiation	167, 163, 10	⊢
	: , : , :
7	instantiation	11, 12, 13, 135, 14, 15	⊢
	: , : , :
8	instantiation	131, 16, 17	⊢
	: , : , :
9	instantiation	93, 18, 19, 20	⊢
	: , : , : , :
10	instantiation	167, 165, 21	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right_strong
12	instantiation	167, 163, 22	⊢
	: , : , :
13	instantiation	167, 23, 24	⊢
	: , : , :
14	instantiation	25, 161, 135, 26, 27, 28	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
16	instantiation	143, 134	⊢
	: , : , :
17	instantiation	29, 123, 155, 30	⊢
	: , : , :
18	instantiation	131, 31, 32	⊢
	: , : , :
19	instantiation	131, 33, 34	⊢
	: , : , :
20	instantiation	66	⊢
	:
21	instantiation	167, 168, 35	⊢
	: , : , :
22	instantiation	167, 165, 36	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
24	instantiation	167, 37, 38	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.multiplication.weak_bound_via_right_factor_bound
26	instantiation	136, 137, 72	⊢
	: , : , :
27	instantiation	39, 72	⊢
	:
28	instantiation	40, 169	⊢
	:
29	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
30	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
31	instantiation	143, 41	⊢
	: , : , :
32	instantiation	131, 42, 43	⊢
	: , : , :
33	instantiation	143, 44	⊢
	: , : , :
34	instantiation	131, 45, 46	⊢
	: , : , :
35	instantiation	47, 48, 162	⊢
	: , :
36	instantiation	167, 168, 49	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
38	instantiation	167, 50, 60	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
40	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
41	instantiation	143, 51	⊢
	: , : , :
42	instantiation	52, 77, 169, 162, 78, 53, 55, 123, 112	⊢
	: , : , : , : , : , :
43	instantiation	54, 123, 55, 56	⊢
	: , : , :
44	instantiation	143, 119	⊢
	: , : , :
45	instantiation	131, 57, 58	⊢
	: , : , :
46	instantiation	154, 80	⊢
	:
47	theorem		⊢
	proveit.numbers.addition.add_nat_closure_bin
48	instantiation	167, 59, 60	⊢
	: , : , :
49	instantiation	61, 169, 162	⊢
	: , :
50	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
51	instantiation	131, 62, 63	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.addition.disassociation
53	instantiation	88	⊢
	: , :
54	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_23
55	instantiation	90, 64, 65	⊢
	: , : , :
56	instantiation	66	⊢
	:
57	instantiation	67, 77, 169, 162, 78, 68, 155, 69, 80	⊢
	: , : , : , : , : , :
58	instantiation	143, 70	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
60	instantiation	71, 159, 72	⊢
	: , :
61	theorem		⊢
	proveit.numbers.multiplication.mult_nat_closure_bin
62	instantiation	143, 73	⊢
	: , : , :
63	instantiation	76, 162, 169, 77, 74, 78, 155, 87, 80	⊢
	: , : , : , : , : , :
64	instantiation	86, 75, 80	⊢
	: , :
65	instantiation	76, 77, 169, 162, 78, 79, 155, 87, 80	⊢
	: , : , : , : , : , :
66	axiom		⊢
	proveit.logic.equality.equals_reflexivity
67	theorem		⊢
	proveit.numbers.multiplication.association
68	instantiation	88	⊢
	: , :
69	instantiation	101, 123, 155, 118	⊢
	: , :
70	instantiation	90, 81, 82	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.multiplication.mult_nat_pos_closure_bin
72	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
73	instantiation	93, 83, 84, 85	⊢
	: , : , : , :
74	instantiation	88	⊢
	: , :
75	instantiation	86, 155, 87	⊢
	: , :
76	theorem		⊢
	proveit.numbers.multiplication.disassociation
77	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
78	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
79	instantiation	88	⊢
	: , :
80	instantiation	167, 160, 89	⊢
	: , : , :
81	instantiation	90, 91, 92	⊢
	: , : , :
82	instantiation	93, 94, 95, 96	⊢
	: , : , : , :
83	instantiation	143, 97	⊢
	: , : , :
84	instantiation	98, 99	⊢
	: , :
85	instantiation	143, 100	⊢
	: , : , :
86	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
87	instantiation	101, 123, 102, 103	⊢
	: , :
88	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
89	instantiation	136, 137, 104	⊢
	: , : , :
90	theorem		⊢
	proveit.logic.equality.sub_right_side_into
91	instantiation	105, 123, 115, 106	⊢
	: , : , : , : , :
92	instantiation	131, 107, 108	⊢
	: , : , :
93	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
94	instantiation	143, 109	⊢
	: , : , :
95	instantiation	143, 109	⊢
	: , : , :
96	instantiation	146, 123	⊢
	:
97	instantiation	110, 111, 112	⊢
	: , :
98	theorem		⊢
	proveit.logic.equality.equals_reversal
99	instantiation	113, 155, 125, 124, 118	⊢
	: , : , :
100	instantiation	114, 115, 153	⊢
	: , :
101	theorem		⊢
	proveit.numbers.division.div_complex_closure
102	instantiation	116, 155, 123	⊢
	: , :
103	instantiation	117, 118, 119	⊢
	: , : , :
104	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
105	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_numer_left
106	instantiation	167, 126, 120	⊢
	: , : , :
107	instantiation	143, 121	⊢
	: , : , :
108	instantiation	143, 122	⊢
	: , : , :
109	instantiation	145, 123	⊢
	:
110	theorem		⊢
	proveit.numbers.addition.commutation
111	instantiation	167, 160, 124	⊢
	: , : , :
112	instantiation	167, 160, 125	⊢
	: , : , :
113	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
114	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
115	instantiation	167, 126, 127	⊢
	: , : , :
116	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
117	theorem		⊢
	proveit.logic.equality.sub_left_side_into
118	instantiation	128, 159	⊢
	:
119	instantiation	129, 155	⊢
	:
120	instantiation	167, 140, 130	⊢
	: , : , :
121	instantiation	131, 132, 133	⊢
	: , : , :
122	instantiation	143, 134	⊢
	: , : , :
123	instantiation	167, 160, 135	⊢
	: , : , :
124	instantiation	136, 137, 138	⊢
	: , : , :
125	instantiation	167, 163, 139	⊢
	: , : , :
126	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
127	instantiation	167, 140, 141	⊢
	: , : , :
128	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
129	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
130	instantiation	167, 151, 142	⊢
	: , : , :
131	axiom		⊢
	proveit.logic.equality.equals_transitivity
132	instantiation	143, 144	⊢
	: , : , :
133	instantiation	145, 155	⊢
	:
134	instantiation	146, 155	⊢
	:
135	instantiation	167, 163, 147	⊢
	: , : , :
136	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
137	instantiation	148, 149	⊢
	: , :
138	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
139	instantiation	167, 165, 150	⊢
	: , : , :
140	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
141	instantiation	167, 151, 152	⊢
	: , : , :
142	instantiation	167, 158, 153	⊢
	: , : , :
143	axiom		⊢
	proveit.logic.equality.substitution
144	instantiation	154, 155	⊢
	:
145	theorem		⊢
	proveit.numbers.division.frac_one_denom
146	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
147	instantiation	167, 165, 157	⊢
	: , : , :
148	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
149	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
150	instantiation	156, 157	⊢
	:
151	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
152	instantiation	167, 158, 159	⊢
	: , : , :
153	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
154	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
155	instantiation	167, 160, 161	⊢
	: , : , :
156	theorem		⊢
	proveit.numbers.negation.int_closure
157	instantiation	167, 168, 162	⊢
	: , : , :
158	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
159	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
160	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
161	instantiation	167, 163, 164	⊢
	: , : , :
162	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
163	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
164	instantiation	167, 165, 166	⊢
	: , : , :
165	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
166	instantiation	167, 168, 169	⊢
	: , : , :
167	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
168	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
169	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements