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_left_side_into
2	instantiation	4, 5, 6	,  ⊢
	: , : , :
3	instantiation	7, 122	⊢
	:
4	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less
5	instantiation	8, 25, 9, 13, 10, 11*	⊢
	: , : , :
6	instantiation	12, 13, 25, 14, 15	,  ⊢
	: , : , :
7	theorem		⊢
	proveit.numbers.addition.elim_zero_left
8	theorem		⊢
	proveit.numbers.addition.weak_bound_via_right_term_bound
9	instantiation	136, 30	⊢
	:
10	instantiation	16, 22, 30, 17	⊢
	: , :
11	instantiation	18, 19, 20, 92, 21	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
13	instantiation	136, 22	⊢
	:
14	instantiation	23, 25, 34, 26	⊢
	: , : , :
15	instantiation	24, 25, 34, 26	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.negation.negated_weak_bound
17	instantiation	27, 53, 33, 52, 28, 29	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.addition.subtraction.negated_add
19	instantiation	151, 129, 34	⊢
	: , : , :
20	instantiation	151, 129, 30	⊢
	: , : , :
21	instantiation	105, 31, 32	⊢
	: , : , :
22	instantiation	43, 33, 53, 47	⊢
	: , :
23	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
24	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
25	instantiation	136, 34	⊢
	:
26	instantiation	35, 36	⊢
	:
27	theorem		⊢
	proveit.numbers.division.weak_div_from_numer_bound__pos_denom
28	instantiation	37, 75, 103, 64	⊢
	: , : , :
29	instantiation	38, 65	⊢
	:
30	instantiation	43, 52, 53, 47	⊢
	: , :
31	instantiation	94, 39	⊢
	: , : , :
32	instantiation	40, 150, 140, 41*	⊢
	: , : , : , :
33	instantiation	151, 144, 42	⊢
	: , : , :
34	instantiation	43, 137, 126, 77	⊢
	: , :
35	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_in_interval
36	assumption		⊢
37	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
38	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
39	instantiation	44, 45, 46, 47, 48*	⊢
	: , :
40	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
41	instantiation	105, 49, 50	⊢
	: , : , :
42	instantiation	151, 149, 51	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.division.div_real_closure
44	theorem		⊢
	proveit.numbers.division.div_as_mult
45	instantiation	151, 129, 52	⊢
	: , : , :
46	instantiation	151, 129, 53	⊢
	: , : , :
47	instantiation	90, 65	⊢
	:
48	instantiation	105, 54, 55	⊢
	: , : , :
49	instantiation	82, 146, 56, 57, 58, 59	⊢
	: , : , : , :
50	instantiation	60, 61, 62	⊢
	:
51	instantiation	151, 63, 64	⊢
	: , : , :
52	instantiation	141, 142, 114	⊢
	: , : , :
53	instantiation	141, 142, 65	⊢
	: , : , :
54	instantiation	94, 66	⊢
	: , : , :
55	instantiation	67, 111, 68, 128, 77, 69*	⊢
	: , : , :
56	instantiation	127	⊢
	: , :
57	instantiation	127	⊢
	: , :
58	instantiation	105, 70, 71	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
60	theorem		⊢
	proveit.numbers.division.frac_cancel_complete
61	instantiation	151, 129, 72	⊢
	: , : , :
62	instantiation	90, 73	⊢
	:
63	instantiation	74, 75, 103	⊢
	: , :
64	assumption		⊢
65	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
66	instantiation	76, 111, 135, 130, 77, 78*	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
68	instantiation	79, 135, 130	⊢
	: , :
69	instantiation	105, 80, 81	⊢
	: , : , :
70	instantiation	82, 146, 83, 84, 85, 86	⊢
	: , : , : , :
71	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
72	instantiation	151, 144, 87	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
74	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
75	instantiation	88, 89, 150	⊢
	: , :
76	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_real_power
77	instantiation	90, 139	⊢
	:
78	instantiation	91, 121, 92, 93*	⊢
	: , :
79	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
80	instantiation	94, 95	⊢
	: , : , :
81	instantiation	96, 97, 98, 99*	⊢
	: , :
82	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
83	instantiation	127	⊢
	: , :
84	instantiation	127	⊢
	: , :
85	instantiation	100, 111	⊢
	:
86	instantiation	104, 111	⊢
	:
87	instantiation	151, 149, 101	⊢
	: , : , :
88	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
89	instantiation	102, 103	⊢
	:
90	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
91	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
92	instantiation	151, 129, 137	⊢
	: , : , :
93	instantiation	104, 121	⊢
	:
94	axiom		⊢
	proveit.logic.equality.substitution
95	instantiation	105, 106, 107	⊢
	: , : , :
96	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
97	instantiation	151, 108, 109	⊢
	: , : , :
98	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
99	instantiation	110, 111	⊢
	:
100	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
101	instantiation	151, 152, 112	⊢
	: , : , :
102	theorem		⊢
	proveit.numbers.negation.int_closure
103	instantiation	151, 113, 114	⊢
	: , : , :
104	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
105	axiom		⊢
	proveit.logic.equality.equals_transitivity
106	instantiation	115, 116, 146, 153, 117, 118, 121, 122, 119	⊢
	: , : , : , : , : , :
107	instantiation	120, 121, 122, 123	⊢
	: , : , :
108	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
109	instantiation	151, 124, 125	⊢
	: , : , :
110	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
111	instantiation	151, 129, 126	⊢
	: , : , :
112	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
113	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
114	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
115	theorem		⊢
	proveit.numbers.addition.disassociation
116	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
117	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
118	instantiation	127	⊢
	: , :
119	instantiation	151, 129, 128	⊢
	: , : , :
120	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
121	instantiation	151, 129, 135	⊢
	: , : , :
122	instantiation	151, 129, 130	⊢
	: , : , :
123	instantiation	131	⊢
	:
124	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
125	instantiation	151, 132, 133	⊢
	: , : , :
126	instantiation	151, 144, 134	⊢
	: , : , :
127	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
128	instantiation	136, 135	⊢
	:
129	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
130	instantiation	136, 137	⊢
	:
131	axiom		⊢
	proveit.logic.equality.equals_reflexivity
132	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
133	instantiation	151, 138, 139	⊢
	: , : , :
134	instantiation	151, 149, 140	⊢
	: , : , :
135	instantiation	141, 142, 143	⊢
	: , : , :
136	theorem		⊢
	proveit.numbers.negation.real_closure
137	instantiation	151, 144, 145	⊢
	: , : , :
138	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
139	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
140	instantiation	151, 152, 146	⊢
	: , : , :
141	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
142	instantiation	147, 148	⊢
	: , :
143	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
144	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
145	instantiation	151, 149, 150	⊢
	: , : , :
146	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
147	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
148	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
149	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
150	instantiation	151, 152, 153	⊢
	: , : , :
151	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
152	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
153	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements