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	⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.number_sets.real_numbers.relax_IntervalCO
2	instantiation	12, 5	⊢
	:
3	reference	5	⊢
4	instantiation	6, 7, 47, 46, 8, 9*, 10*, 17*	⊢
	: , : , : , :
5	instantiation	116, 105, 11	⊢
	: , : , :
6	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rescale_interval_co_membership
7	instantiation	12, 47	⊢
	:
8	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_round_in_interval
9	instantiation	58, 13, 14, 15	⊢
	: , : , : , :
10	instantiation	16, 35, 36, 17*	⊢
	: , :
11	instantiation	18, 106, 19, 20	⊢
	: , :
12	theorem		⊢
	proveit.numbers.negation.real_closure
13	instantiation	21, 118, 107, 29, 22, 30, 35, 111, 32	⊢
	: , : , : , : , : , :
14	instantiation	93, 23, 24	⊢
	: , : , :
15	instantiation	101, 32	⊢
	:
16	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
17	instantiation	93, 25, 26	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.division.div_rational_closure
19	instantiation	116, 112, 27	⊢
	: , : , :
20	instantiation	76, 41	⊢
	:
21	theorem		⊢
	proveit.numbers.multiplication.disassociation
22	instantiation	42	⊢
	: , :
23	instantiation	28, 29, 107, 118, 30, 31, 35, 111, 32	⊢
	: , : , : , : , : , :
24	instantiation	102, 33	⊢
	: , : , :
25	instantiation	34, 35, 36	⊢
	: , :
26	instantiation	37, 86, 38, 72, 61*, 39*	⊢
	: , : , : , :
27	instantiation	116, 40, 41	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.multiplication.association
29	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
30	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
31	instantiation	42	⊢
	: , :
32	instantiation	116, 114, 43	⊢
	: , : , :
33	instantiation	55, 44, 45	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.multiplication.commutation
35	instantiation	116, 114, 46	⊢
	: , : , :
36	instantiation	116, 114, 47	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.division.prod_of_fracs
38	instantiation	116, 82, 48	⊢
	: , : , :
39	instantiation	49, 67, 108, 80, 50*	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
41	instantiation	51, 107, 52	⊢
	: , :
42	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
43	instantiation	53, 54	⊢
	:
44	instantiation	55, 56, 57	⊢
	: , : , :
45	instantiation	58, 59, 60, 61	⊢
	: , : , : , :
46	instantiation	63, 96, 115, 62	⊢
	: , :
47	instantiation	63, 96, 78, 64	⊢
	: , :
48	instantiation	116, 90, 65	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.exponentiation.product_of_posnat_powers
50	instantiation	66, 67	⊢
	:
51	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
52	instantiation	68, 118, 69	⊢
	: , :
53	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
54	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int
55	theorem		⊢
	proveit.logic.equality.sub_right_side_into
56	instantiation	70, 86, 71, 72	⊢
	: , : , : , : , :
57	instantiation	93, 73, 74	⊢
	: , : , :
58	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
59	instantiation	102, 75	⊢
	: , : , :
60	instantiation	102, 75	⊢
	: , : , :
61	instantiation	110, 86	⊢
	:
62	instantiation	76, 121	⊢
	:
63	theorem		⊢
	proveit.numbers.division.div_real_closure
64	instantiation	76, 87	⊢
	:
65	instantiation	116, 99, 77	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
67	instantiation	116, 114, 78	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.addition.add_nat_closure_bin
69	instantiation	116, 79, 80	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_denom_left
71	instantiation	116, 82, 81	⊢
	: , : , :
72	instantiation	116, 82, 83	⊢
	: , : , :
73	instantiation	102, 84	⊢
	: , : , :
74	instantiation	102, 85	⊢
	: , : , :
75	instantiation	104, 86	⊢
	:
76	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
77	instantiation	116, 109, 87	⊢
	: , : , :
78	instantiation	116, 105, 88	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
80	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
81	instantiation	116, 90, 89	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
83	instantiation	116, 90, 91	⊢
	: , : , :
84	instantiation	102, 92	⊢
	: , : , :
85	instantiation	93, 94, 95	⊢
	: , : , :
86	instantiation	116, 114, 96	⊢
	: , : , :
87	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
88	instantiation	116, 112, 97	⊢
	: , : , :
89	instantiation	116, 99, 98	⊢
	: , : , :
90	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
91	instantiation	116, 99, 100	⊢
	: , : , :
92	instantiation	101, 111	⊢
	:
93	axiom		⊢
	proveit.logic.equality.equals_transitivity
94	instantiation	102, 103	⊢
	: , : , :
95	instantiation	104, 111	⊢
	:
96	instantiation	116, 105, 106	⊢
	: , : , :
97	instantiation	116, 117, 107	⊢
	: , : , :
98	instantiation	116, 109, 108	⊢
	: , : , :
99	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
100	instantiation	116, 109, 121	⊢
	: , : , :
101	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
102	axiom		⊢
	proveit.logic.equality.substitution
103	instantiation	110, 111	⊢
	:
104	theorem		⊢
	proveit.numbers.division.frac_one_denom
105	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
106	instantiation	116, 112, 113	⊢
	: , : , :
107	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
108	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
109	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
110	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
111	instantiation	116, 114, 115	⊢
	: , : , :
112	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
113	instantiation	116, 117, 118	⊢
	: , : , :
114	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
115	instantiation	119, 120, 121	⊢
	: , : , :
116	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
117	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
118	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
119	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
120	instantiation	122, 123	⊢
	: , :
121	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
122	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
123	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
*equality replacement requirements