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