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.equality.sub_right_side_into
2	instantiation	4, 66, 59, 5, 6, 7, 8*	⊢
	: , : , :
3	instantiation	9, 10, 72, 51, 28, 11*	⊢
	: , : , :
4	theorem		⊢
	proveit.numbers.division.weak_div_from_numer_bound__pos_denom
5	instantiation	77, 25, 24	⊢
	: , :
6	instantiation	12, 13, 14	⊢
	: , : , :
7	instantiation	15, 93	⊢
	:
8	instantiation	16, 70, 51, 28, 17*	⊢
	: , :
9	theorem		⊢
	proveit.numbers.division.distribute_frac_through_subtract
10	instantiation	156, 122, 25	⊢
	: , : , :
11	instantiation	97, 18, 19	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less_eq
13	instantiation	20, 45, 59, 24, 21, 22*	⊢
	: , : , :
14	instantiation	23, 24, 45, 25, 26	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
16	theorem		⊢
	proveit.numbers.division.neg_frac_neg_numerator
17	instantiation	27, 70, 51, 28, 29*	⊢
	: , :
18	instantiation	30, 31, 32, 35, 33*	⊢
	: , : , :
19	instantiation	34, 35	⊢
	:
20	theorem		⊢
	proveit.numbers.addition.weak_bound_via_right_term_bound
21	instantiation	36, 123, 83, 82, 37, 38, 39*, 40*	⊢
	: , : , :
22	instantiation	41, 42	⊢
	:
23	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
24	instantiation	131, 83	⊢
	:
25	instantiation	43, 45, 95, 46	⊢
	: , : , :
26	instantiation	44, 45, 95, 46	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.division.div_as_mult
28	instantiation	84, 93	⊢
	:
29	instantiation	97, 47, 48	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.division.frac_cancel_left
31	instantiation	156, 100, 49	⊢
	: , : , :
32	instantiation	156, 100, 50	⊢
	: , : , :
33	instantiation	96, 51	⊢
	:
34	theorem		⊢
	proveit.numbers.division.frac_one_denom
35	instantiation	156, 122, 52	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.multiplication.reversed_weak_bound_via_right_factor_bound
37	instantiation	53, 130, 149, 119	⊢
	: , : , :
38	instantiation	54, 55	⊢
	: , :
39	instantiation	57, 86, 70, 56*	⊢
	: , :
40	instantiation	57, 86, 72, 58*	⊢
	: , :
41	theorem		⊢
	proveit.numbers.addition.elim_zero_left
42	instantiation	156, 122, 59	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
44	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
45	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
46	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval
47	instantiation	88, 60	⊢
	: , : , :
48	instantiation	61, 103, 62, 121, 75, 63*	⊢
	: , : , :
49	instantiation	156, 115, 64	⊢
	: , : , :
50	instantiation	156, 115, 65	⊢
	: , : , :
51	instantiation	156, 122, 66	⊢
	: , : , :
52	instantiation	67, 68	⊢
	:
53	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
54	theorem		⊢
	proveit.numbers.ordering.relax_less
55	instantiation	69, 155	⊢
	:
56	instantiation	71, 70	⊢
	:
57	theorem		⊢
	proveit.numbers.multiplication.mult_neg_left
58	instantiation	71, 72	⊢
	:
59	instantiation	156, 127, 73	⊢
	: , : , :
60	instantiation	74, 103, 132, 123, 75, 76*	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
62	instantiation	77, 132, 123	⊢
	: , :
63	instantiation	97, 78, 79	⊢
	: , : , :
64	instantiation	156, 125, 80	⊢
	: , : , :
65	instantiation	156, 125, 81	⊢
	: , : , :
66	instantiation	142, 143, 93	⊢
	: , : , :
67	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
68	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
69	theorem		⊢
	proveit.numbers.number_sets.integers.negative_if_in_neg_int
70	instantiation	156, 122, 82	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
72	instantiation	156, 122, 83	⊢
	: , : , :
73	instantiation	156, 137, 140	⊢
	: , : , :
74	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_real_power
75	instantiation	84, 136	⊢
	:
76	instantiation	85, 112, 86, 87*	⊢
	: , :
77	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
78	instantiation	88, 89	⊢
	: , : , :
79	instantiation	90, 91, 160, 92*	⊢
	: , :
80	instantiation	156, 135, 93	⊢
	: , : , :
81	instantiation	156, 135, 160	⊢
	: , : , :
82	instantiation	142, 143, 158	⊢
	: , : , :
83	instantiation	156, 127, 94	⊢
	: , : , :
84	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
85	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
86	instantiation	156, 122, 95	⊢
	: , : , :
87	instantiation	96, 112	⊢
	:
88	axiom		⊢
	proveit.logic.equality.substitution
89	instantiation	97, 98, 99	⊢
	: , : , :
90	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
91	instantiation	156, 100, 101	⊢
	: , : , :
92	instantiation	102, 103	⊢
	:
93	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
94	instantiation	156, 137, 104	⊢
	: , : , :
95	instantiation	156, 127, 105	⊢
	: , : , :
96	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
97	axiom		⊢
	proveit.logic.equality.equals_transitivity
98	instantiation	106, 107, 147, 151, 108, 109, 112, 113, 110	⊢
	: , : , : , : , : , :
99	instantiation	111, 112, 113, 114	⊢
	: , : , :
100	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
101	instantiation	156, 115, 116	⊢
	: , : , :
102	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
103	instantiation	156, 122, 117	⊢
	: , : , :
104	instantiation	156, 118, 119	⊢
	: , : , :
105	instantiation	156, 137, 141	⊢
	: , : , :
106	theorem		⊢
	proveit.numbers.addition.disassociation
107	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
108	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
109	instantiation	120	⊢
	: , :
110	instantiation	156, 122, 121	⊢
	: , : , :
111	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
112	instantiation	156, 122, 132	⊢
	: , : , :
113	instantiation	156, 122, 123	⊢
	: , : , :
114	instantiation	124	⊢
	:
115	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
116	instantiation	156, 125, 126	⊢
	: , : , :
117	instantiation	156, 127, 128	⊢
	: , : , :
118	instantiation	129, 130, 149	⊢
	: , :
119	assumption		⊢
120	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
121	instantiation	131, 132	⊢
	:
122	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
123	instantiation	156, 133, 134	⊢
	: , : , :
124	axiom		⊢
	proveit.logic.equality.equals_reflexivity
125	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
126	instantiation	156, 135, 136	⊢
	: , : , :
127	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
128	instantiation	156, 137, 138	⊢
	: , : , :
129	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
130	instantiation	139, 140, 141	⊢
	: , :
131	theorem		⊢
	proveit.numbers.negation.real_closure
132	instantiation	142, 143, 144	⊢
	: , : , :
133	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
134	instantiation	156, 145, 146	⊢
	: , : , :
135	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
136	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
137	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
138	instantiation	156, 150, 147	⊢
	: , : , :
139	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
140	instantiation	148, 149	⊢
	:
141	instantiation	156, 150, 151	⊢
	: , : , :
142	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
143	instantiation	152, 153	⊢
	: , :
144	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
145	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_neg_within_real_neg
146	instantiation	156, 154, 155	⊢
	: , : , :
147	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
148	theorem		⊢
	proveit.numbers.negation.int_closure
149	instantiation	156, 157, 158	⊢
	: , : , :
150	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
151	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
152	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
153	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
154	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.neg_int_within_rational_neg
155	instantiation	159, 160	⊢
	:
156	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
157	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
158	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
159	theorem		⊢
	proveit.numbers.negation.int_neg_closure
160	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
*equality replacement requirements