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.numbers.ordering.transitivity_less_eq_less
2	instantiation	4, 21, 5, 9, 6, 7*	⊢
	: , : , :
3	instantiation	8, 9, 21, 10, 11	,  ⊢
	: , : , :
4	theorem		⊢
	proveit.numbers.addition.weak_bound_via_right_term_bound
5	instantiation	132, 26	⊢
	:
6	instantiation	12, 18, 26, 13	⊢
	: , :
7	instantiation	14, 15, 16, 88, 17	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
9	instantiation	132, 18	⊢
	:
10	instantiation	19, 21, 30, 22	⊢
	: , : , :
11	instantiation	20, 21, 30, 22	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.negation.negated_weak_bound
13	instantiation	23, 49, 29, 48, 24, 25	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.addition.subtraction.negated_add
15	instantiation	147, 125, 30	⊢
	: , : , :
16	instantiation	147, 125, 26	⊢
	: , : , :
17	instantiation	101, 27, 28	⊢
	: , : , :
18	instantiation	39, 29, 49, 43	⊢
	: , :
19	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
20	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
21	instantiation	132, 30	⊢
	:
22	instantiation	31, 32	⊢
	:
23	theorem		⊢
	proveit.numbers.division.weak_div_from_numer_bound__pos_denom
24	instantiation	33, 71, 99, 60	⊢
	: , : , :
25	instantiation	34, 61	⊢
	:
26	instantiation	39, 48, 49, 43	⊢
	: , :
27	instantiation	90, 35	⊢
	: , : , :
28	instantiation	36, 146, 136, 37*	⊢
	: , : , : , :
29	instantiation	147, 140, 38	⊢
	: , : , :
30	instantiation	39, 133, 122, 73	⊢
	: , :
31	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_in_interval
32	assumption		⊢
33	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
34	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
35	instantiation	40, 41, 42, 43, 44*	⊢
	: , :
36	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
37	instantiation	101, 45, 46	⊢
	: , : , :
38	instantiation	147, 145, 47	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.division.div_real_closure
40	theorem		⊢
	proveit.numbers.division.div_as_mult
41	instantiation	147, 125, 48	⊢
	: , : , :
42	instantiation	147, 125, 49	⊢
	: , : , :
43	instantiation	86, 61	⊢
	:
44	instantiation	101, 50, 51	⊢
	: , : , :
45	instantiation	78, 142, 52, 53, 54, 55	⊢
	: , : , : , :
46	instantiation	56, 57, 58	⊢
	:
47	instantiation	147, 59, 60	⊢
	: , : , :
48	instantiation	137, 138, 110	⊢
	: , : , :
49	instantiation	137, 138, 61	⊢
	: , : , :
50	instantiation	90, 62	⊢
	: , : , :
51	instantiation	63, 107, 64, 124, 73, 65*	⊢
	: , : , :
52	instantiation	123	⊢
	: , :
53	instantiation	123	⊢
	: , :
54	instantiation	101, 66, 67	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
56	theorem		⊢
	proveit.numbers.division.frac_cancel_complete
57	instantiation	147, 125, 68	⊢
	: , : , :
58	instantiation	86, 69	⊢
	:
59	instantiation	70, 71, 99	⊢
	: , :
60	assumption		⊢
61	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
62	instantiation	72, 107, 131, 126, 73, 74*	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
64	instantiation	75, 131, 126	⊢
	: , :
65	instantiation	101, 76, 77	⊢
	: , : , :
66	instantiation	78, 142, 79, 80, 81, 82	⊢
	: , : , : , :
67	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
68	instantiation	147, 140, 83	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
70	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
71	instantiation	84, 85, 146	⊢
	: , :
72	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_real_power
73	instantiation	86, 135	⊢
	:
74	instantiation	87, 117, 88, 89*	⊢
	: , :
75	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
76	instantiation	90, 91	⊢
	: , : , :
77	instantiation	92, 93, 94, 95*	⊢
	: , :
78	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
79	instantiation	123	⊢
	: , :
80	instantiation	123	⊢
	: , :
81	instantiation	96, 107	⊢
	:
82	instantiation	100, 107	⊢
	:
83	instantiation	147, 145, 97	⊢
	: , : , :
84	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
85	instantiation	98, 99	⊢
	:
86	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
87	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
88	instantiation	147, 125, 133	⊢
	: , : , :
89	instantiation	100, 117	⊢
	:
90	axiom		⊢
	proveit.logic.equality.substitution
91	instantiation	101, 102, 103	⊢
	: , : , :
92	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
93	instantiation	147, 104, 105	⊢
	: , : , :
94	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
95	instantiation	106, 107	⊢
	:
96	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
97	instantiation	147, 148, 108	⊢
	: , : , :
98	theorem		⊢
	proveit.numbers.negation.int_closure
99	instantiation	147, 109, 110	⊢
	: , : , :
100	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
101	axiom		⊢
	proveit.logic.equality.equals_transitivity
102	instantiation	111, 112, 142, 149, 113, 114, 117, 118, 115	⊢
	: , : , : , : , : , :
103	instantiation	116, 117, 118, 119	⊢
	: , : , :
104	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
105	instantiation	147, 120, 121	⊢
	: , : , :
106	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
107	instantiation	147, 125, 122	⊢
	: , : , :
108	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
109	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
110	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
111	theorem		⊢
	proveit.numbers.addition.disassociation
112	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
113	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
114	instantiation	123	⊢
	: , :
115	instantiation	147, 125, 124	⊢
	: , : , :
116	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
117	instantiation	147, 125, 131	⊢
	: , : , :
118	instantiation	147, 125, 126	⊢
	: , : , :
119	instantiation	127	⊢
	:
120	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
121	instantiation	147, 128, 129	⊢
	: , : , :
122	instantiation	147, 140, 130	⊢
	: , : , :
123	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
124	instantiation	132, 131	⊢
	:
125	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
126	instantiation	132, 133	⊢
	:
127	axiom		⊢
	proveit.logic.equality.equals_reflexivity
128	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
129	instantiation	147, 134, 135	⊢
	: , : , :
130	instantiation	147, 145, 136	⊢
	: , : , :
131	instantiation	137, 138, 139	⊢
	: , : , :
132	theorem		⊢
	proveit.numbers.negation.real_closure
133	instantiation	147, 140, 141	⊢
	: , : , :
134	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
135	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
136	instantiation	147, 148, 142	⊢
	: , : , :
137	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
138	instantiation	143, 144	⊢
	: , :
139	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
140	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
141	instantiation	147, 145, 146	⊢
	: , : , :
142	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
143	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
144	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
145	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
146	instantiation	147, 148, 149	⊢
	: , : , :
147	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
148	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
149	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements