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.interval_cc_lower_bound
2	reference	6	⊢
3	reference	8	⊢
4	instantiation	5, 6, 8, 7	⊢
	: , : , :
5	theorem		⊢
	proveit.numbers.number_sets.real_numbers.relax_IntervalCO
6	instantiation	15, 8	⊢
	:
7	instantiation	9, 10, 50, 49, 11, 12*, 13*, 20*	⊢
	: , : , : , :
8	instantiation	119, 108, 14	⊢
	: , : , :
9	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rescale_interval_co_membership
10	instantiation	15, 50	⊢
	:
11	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_round_in_interval
12	instantiation	61, 16, 17, 18	⊢
	: , : , : , :
13	instantiation	19, 38, 39, 20*	⊢
	: , :
14	instantiation	21, 109, 22, 23	⊢
	: , :
15	theorem		⊢
	proveit.numbers.negation.real_closure
16	instantiation	24, 121, 110, 32, 25, 33, 38, 114, 35	⊢
	: , : , : , : , : , :
17	instantiation	96, 26, 27	⊢
	: , : , :
18	instantiation	104, 35	⊢
	:
19	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
20	instantiation	96, 28, 29	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.division.div_rational_closure
22	instantiation	119, 115, 30	⊢
	: , : , :
23	instantiation	79, 44	⊢
	:
24	theorem		⊢
	proveit.numbers.multiplication.disassociation
25	instantiation	45	⊢
	: , :
26	instantiation	31, 32, 110, 121, 33, 34, 38, 114, 35	⊢
	: , : , : , : , : , :
27	instantiation	105, 36	⊢
	: , : , :
28	instantiation	37, 38, 39	⊢
	: , :
29	instantiation	40, 89, 41, 75, 64*, 42*	⊢
	: , : , : , :
30	instantiation	119, 43, 44	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.multiplication.association
32	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
33	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
34	instantiation	45	⊢
	: , :
35	instantiation	119, 117, 46	⊢
	: , : , :
36	instantiation	58, 47, 48	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.multiplication.commutation
38	instantiation	119, 117, 49	⊢
	: , : , :
39	instantiation	119, 117, 50	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.division.prod_of_fracs
41	instantiation	119, 85, 51	⊢
	: , : , :
42	instantiation	52, 70, 111, 83, 53*	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
44	instantiation	54, 110, 55	⊢
	: , :
45	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
46	instantiation	56, 57	⊢
	:
47	instantiation	58, 59, 60	⊢
	: , : , :
48	instantiation	61, 62, 63, 64	⊢
	: , : , : , :
49	instantiation	66, 99, 118, 65	⊢
	: , :
50	instantiation	66, 99, 81, 67	⊢
	: , :
51	instantiation	119, 93, 68	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.exponentiation.product_of_posnat_powers
53	instantiation	69, 70	⊢
	:
54	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
55	instantiation	71, 121, 72	⊢
	: , :
56	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
57	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int
58	theorem		⊢
	proveit.logic.equality.sub_right_side_into
59	instantiation	73, 89, 74, 75	⊢
	: , : , : , : , :
60	instantiation	96, 76, 77	⊢
	: , : , :
61	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
62	instantiation	105, 78	⊢
	: , : , :
63	instantiation	105, 78	⊢
	: , : , :
64	instantiation	113, 89	⊢
	:
65	instantiation	79, 124	⊢
	:
66	theorem		⊢
	proveit.numbers.division.div_real_closure
67	instantiation	79, 90	⊢
	:
68	instantiation	119, 102, 80	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
70	instantiation	119, 117, 81	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.addition.add_nat_closure_bin
72	instantiation	119, 82, 83	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_denom_left
74	instantiation	119, 85, 84	⊢
	: , : , :
75	instantiation	119, 85, 86	⊢
	: , : , :
76	instantiation	105, 87	⊢
	: , : , :
77	instantiation	105, 88	⊢
	: , : , :
78	instantiation	107, 89	⊢
	:
79	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
80	instantiation	119, 112, 90	⊢
	: , : , :
81	instantiation	119, 108, 91	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
83	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
84	instantiation	119, 93, 92	⊢
	: , : , :
85	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
86	instantiation	119, 93, 94	⊢
	: , : , :
87	instantiation	105, 95	⊢
	: , : , :
88	instantiation	96, 97, 98	⊢
	: , : , :
89	instantiation	119, 117, 99	⊢
	: , : , :
90	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
91	instantiation	119, 115, 100	⊢
	: , : , :
92	instantiation	119, 102, 101	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
94	instantiation	119, 102, 103	⊢
	: , : , :
95	instantiation	104, 114	⊢
	:
96	axiom		⊢
	proveit.logic.equality.equals_transitivity
97	instantiation	105, 106	⊢
	: , : , :
98	instantiation	107, 114	⊢
	:
99	instantiation	119, 108, 109	⊢
	: , : , :
100	instantiation	119, 120, 110	⊢
	: , : , :
101	instantiation	119, 112, 111	⊢
	: , : , :
102	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
103	instantiation	119, 112, 124	⊢
	: , : , :
104	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
105	axiom		⊢
	proveit.logic.equality.substitution
106	instantiation	113, 114	⊢
	:
107	theorem		⊢
	proveit.numbers.division.frac_one_denom
108	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
109	instantiation	119, 115, 116	⊢
	: , : , :
110	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
111	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
112	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
113	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
114	instantiation	119, 117, 118	⊢
	: , : , :
115	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
116	instantiation	119, 120, 121	⊢
	: , : , :
117	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
118	instantiation	122, 123, 124	⊢
	: , : , :
119	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
120	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
121	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
122	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
123	instantiation	125, 126	⊢
	: , :
124	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
125	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
126	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
*equality replacement requirements