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	⊢
	: , :
1	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
2	instantiation	4, 45, 49, 5, 6, 7*, 8*	⊢
	: , : , :
3	instantiation	9, 10	⊢
	: , :
4	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
5	instantiation	11, 99, 13	⊢
	: , :
6	instantiation	12, 49, 99, 13, 14, 15	⊢
	: , : , :
7	instantiation	107, 16, 17	⊢
	: , : , :
8	instantiation	132, 18, 19	⊢
	: , : , :
9	theorem		⊢
	proveit.numbers.ordering.relax_less
10	instantiation	20, 21, 22	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
12	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right_strong
13	instantiation	153, 143, 23	⊢
	: , : , :
14	instantiation	24, 49, 36, 37	⊢
	: , : , :
15	instantiation	25, 44	⊢
	:
16	instantiation	26, 31	⊢
	:
17	instantiation	27, 31, 28	⊢
	: , :
18	instantiation	29, 90, 114, 155, 91, 30, 94, 33, 31	⊢
	: , : , : , : , : , :
19	instantiation	32, 33, 94, 34	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
21	instantiation	35, 49, 36, 37	⊢
	: , : , :
22	instantiation	38, 39, 40, 41, 42	⊢
	: , : , :
23	instantiation	153, 43, 44	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
25	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
26	theorem		⊢
	proveit.numbers.addition.elim_zero_right
27	theorem		⊢
	proveit.numbers.addition.commutation
28	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
29	theorem		⊢
	proveit.numbers.addition.disassociation
30	instantiation	97	⊢
	: , :
31	instantiation	153, 151, 45	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_23
33	instantiation	153, 151, 67	⊢
	: , : , :
34	instantiation	46	⊢
	:
35	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
36	instantiation	153, 143, 47	⊢
	: , : , :
37	instantiation	48, 49, 135, 98, 50, 51*, 52*, 53*	⊢
	: , : , : , :
38	theorem		⊢
	proveit.numbers.division.weak_div_from_denom_bound__all_pos
39	instantiation	153, 54, 55	⊢
	: , : , :
40	instantiation	153, 56, 65	⊢
	: , : , :
41	instantiation	153, 56, 57	⊢
	: , : , :
42	instantiation	58, 86, 135, 59, 60, 61, 62*	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
44	instantiation	63, 64, 65	⊢
	: , :
45	instantiation	66, 67	⊢
	:
46	axiom		⊢
	proveit.logic.equality.equals_reflexivity
47	instantiation	68, 144, 69, 104	⊢
	: , :
48	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rescale_interval_co_membership
49	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
50	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval
51	instantiation	110, 70, 71, 72	⊢
	: , : , : , :
52	instantiation	73, 93	⊢
	:
53	instantiation	147, 93	⊢
	:
54	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg
55	instantiation	153, 74, 155	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
57	instantiation	153, 79, 158	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.exponentiation.exp_monotonicity_large_base_less_eq
59	instantiation	156, 157, 76	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
61	instantiation	75, 76	⊢
	:
62	instantiation	77, 78	⊢
	:
63	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
64	instantiation	153, 79, 145	⊢
	: , : , :
65	instantiation	153, 79, 87	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.negation.real_closure
67	instantiation	103, 135, 86, 80	⊢
	: , :
68	theorem		⊢
	proveit.numbers.division.div_rational_closure
69	instantiation	153, 149, 81	⊢
	: , : , :
70	instantiation	82, 155, 114, 90, 83, 91, 93, 148, 94	⊢
	: , : , : , : , : , :
71	instantiation	132, 84, 85	⊢
	: , : , :
72	instantiation	139, 94	⊢
	:
73	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
74	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg
75	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
76	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
77	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
78	instantiation	153, 151, 86	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
80	instantiation	115, 87	⊢
	:
81	instantiation	153, 88, 158	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.multiplication.disassociation
83	instantiation	97	⊢
	: , :
84	instantiation	89, 90, 114, 155, 91, 92, 93, 148, 94	⊢
	: , : , : , : , : , :
85	instantiation	140, 95	⊢
	: , : , :
86	instantiation	153, 143, 96	⊢
	: , : , :
87	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
88	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
89	theorem		⊢
	proveit.numbers.multiplication.association
90	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
91	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
92	instantiation	97	⊢
	: , :
93	instantiation	153, 151, 98	⊢
	: , : , :
94	instantiation	153, 151, 99	⊢
	: , : , :
95	instantiation	107, 100, 101	⊢
	: , : , :
96	instantiation	153, 149, 102	⊢
	: , : , :
97	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
98	instantiation	103, 135, 152, 104	⊢
	: , :
99	instantiation	105, 106	⊢
	:
100	instantiation	107, 108, 109	⊢
	: , : , :
101	instantiation	110, 111, 112, 113	⊢
	: , : , : , :
102	instantiation	153, 154, 114	⊢
	: , : , :
103	theorem		⊢
	proveit.numbers.division.div_real_closure
104	instantiation	115, 158	⊢
	:
105	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
106	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
107	theorem		⊢
	proveit.logic.equality.sub_right_side_into
108	instantiation	116, 127, 117, 118	⊢
	: , : , : , : , :
109	instantiation	132, 119, 120	⊢
	: , : , :
110	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
111	instantiation	140, 121	⊢
	: , : , :
112	instantiation	140, 121	⊢
	: , : , :
113	instantiation	147, 127	⊢
	:
114	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
115	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
116	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_denom_left
117	instantiation	153, 123, 122	⊢
	: , : , :
118	instantiation	153, 123, 124	⊢
	: , : , :
119	instantiation	140, 125	⊢
	: , : , :
120	instantiation	140, 126	⊢
	: , : , :
121	instantiation	142, 127	⊢
	:
122	instantiation	153, 129, 128	⊢
	: , : , :
123	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
124	instantiation	153, 129, 130	⊢
	: , : , :
125	instantiation	140, 131	⊢
	: , : , :
126	instantiation	132, 133, 134	⊢
	: , : , :
127	instantiation	153, 151, 135	⊢
	: , : , :
128	instantiation	153, 137, 136	⊢
	: , : , :
129	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
130	instantiation	153, 137, 138	⊢
	: , : , :
131	instantiation	139, 148	⊢
	:
132	axiom		⊢
	proveit.logic.equality.equals_transitivity
133	instantiation	140, 141	⊢
	: , : , :
134	instantiation	142, 148	⊢
	:
135	instantiation	153, 143, 144	⊢
	: , : , :
136	instantiation	153, 146, 145	⊢
	: , : , :
137	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
138	instantiation	153, 146, 158	⊢
	: , : , :
139	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
140	axiom		⊢
	proveit.logic.equality.substitution
141	instantiation	147, 148	⊢
	:
142	theorem		⊢
	proveit.numbers.division.frac_one_denom
143	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
144	instantiation	153, 149, 150	⊢
	: , : , :
145	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
146	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
147	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
148	instantiation	153, 151, 152	⊢
	: , : , :
149	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
150	instantiation	153, 154, 155	⊢
	: , : , :
151	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
152	instantiation	156, 157, 158	⊢
	: , : , :
153	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
154	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
155	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
156	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
157	instantiation	159, 160	⊢
	: , :
158	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
159	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
160	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
*equality replacement requirements