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