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	reference	52	⊢
2	instantiation	4, 5, 112, 28, 6, 7	⊢
	: , : , :
3	reference	9	⊢
4	theorem		⊢
	proveit.numbers.ordering.less_add_right_weak_int
5	instantiation	8, 110, 9	⊢
	: , : , :
6	instantiation	10, 107, 75, 84, 11, 12, 83*	⊢
	: , : , :
7	instantiation	13, 14, 15	⊢
	: , :
8	theorem		⊢
	proveit.logic.equality.sub_left_side_into
9	instantiation	16, 107, 75, 86, 17, 18*	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.multiplication.strong_bound_via_right_factor_bound
11	instantiation	19, 20, 84, 21	⊢
	: , : , :
12	instantiation	22, 118	⊢
	:
13	theorem		⊢
	proveit.numbers.ordering.relax_equal_to_less_eq
14	instantiation	116, 95, 23	⊢
	: , : , :
15	instantiation	76	⊢
	:
16	theorem		⊢
	proveit.numbers.multiplication.left_mult_eq_real
17	instantiation	24, 25	⊢
	: , :
18	instantiation	52, 26, 27	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
20	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
21	axiom		⊢
	proveit.physics.quantum.QPE._phase_in_interval
22	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
23	instantiation	116, 111, 28	⊢
	: , : , :
24	theorem		⊢
	proveit.logic.equality.equals_reversal
25	instantiation	29, 96, 40, 30, 41, 31*, 32*	⊢
	: , : , :
26	instantiation	52, 33, 34	⊢
	: , : , :
27	instantiation	35, 36, 37, 38	⊢
	: , : , : , :
28	instantiation	39, 101	⊢
	:
29	theorem		⊢
	proveit.numbers.addition.right_add_eq_rational
30	instantiation	52, 40, 41	⊢
	: , : , :
31	instantiation	42, 74	⊢
	:
32	instantiation	80, 43, 44	⊢
	: , : , :
33	instantiation	45, 69, 70, 46, 47	⊢
	: , : , : , : , :
34	instantiation	80, 48, 49	⊢
	: , : , :
35	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
36	instantiation	90, 50	⊢
	: , : , :
37	instantiation	90, 51	⊢
	: , : , :
38	instantiation	99, 70	⊢
	:
39	theorem		⊢
	proveit.numbers.negation.int_closure
40	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.zero_is_rational
41	instantiation	52, 53, 54	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.addition.elim_zero_left
43	instantiation	55, 56, 57, 109, 58, 59, 62, 60, 74	⊢
	: , : , : , : , : , :
44	instantiation	61, 74, 62, 63	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_numer_left
46	instantiation	116, 65, 64	⊢
	: , : , :
47	instantiation	116, 65, 66	⊢
	: , : , :
48	instantiation	90, 67	⊢
	: , : , :
49	instantiation	90, 68	⊢
	: , : , :
50	instantiation	92, 69	⊢
	:
51	instantiation	92, 70	⊢
	:
52	theorem		⊢
	proveit.logic.equality.sub_right_side_into
53	instantiation	71, 110	⊢
	:
54	assumption		⊢
55	theorem		⊢
	proveit.numbers.addition.disassociation
56	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
57	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
58	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
59	instantiation	72	⊢
	: , :
60	instantiation	73, 74	⊢
	:
61	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
62	instantiation	116, 106, 75	⊢
	: , : , :
63	instantiation	76	⊢
	:
64	instantiation	116, 78, 77	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
66	instantiation	116, 78, 79	⊢
	: , : , :
67	instantiation	80, 81, 82	⊢
	: , : , :
68	instantiation	90, 83	⊢
	: , : , :
69	instantiation	116, 106, 84	⊢
	: , : , :
70	instantiation	116, 106, 85	⊢
	: , : , :
71	axiom		⊢
	proveit.physics.quantum.QPE._delta_b_def
72	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
73	theorem		⊢
	proveit.numbers.negation.complex_closure
74	instantiation	116, 106, 86	⊢
	: , : , :
75	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
76	axiom		⊢
	proveit.logic.equality.equals_reflexivity
77	instantiation	116, 88, 87	⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
79	instantiation	116, 88, 89	⊢
	: , : , :
80	axiom		⊢
	proveit.logic.equality.equals_transitivity
81	instantiation	90, 91	⊢
	: , : , :
82	instantiation	92, 100	⊢
	:
83	instantiation	93, 100	⊢
	:
84	instantiation	116, 95, 94	⊢
	: , : , :
85	instantiation	116, 95, 103	⊢
	: , : , :
86	instantiation	116, 95, 96	⊢
	: , : , :
87	instantiation	116, 97, 118	⊢
	: , : , :
88	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
89	instantiation	116, 97, 98	⊢
	: , : , :
90	axiom		⊢
	proveit.logic.equality.substitution
91	instantiation	99, 100	⊢
	:
92	theorem		⊢
	proveit.numbers.division.frac_one_denom
93	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
94	instantiation	116, 111, 101	⊢
	: , : , :
95	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
96	instantiation	102, 103, 104, 105	⊢
	: , :
97	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
98	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
99	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
100	instantiation	116, 106, 107	⊢
	: , : , :
101	instantiation	116, 108, 109	⊢
	: , : , :
102	theorem		⊢
	proveit.numbers.division.div_rational_closure
103	instantiation	116, 111, 110	⊢
	: , : , :
104	instantiation	116, 111, 112	⊢
	: , : , :
105	instantiation	113, 118	⊢
	:
106	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
107	instantiation	114, 115, 118	⊢
	: , : , :
108	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
109	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
110	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int
111	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
112	instantiation	116, 117, 118	⊢
	: , : , :
113	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
114	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
115	instantiation	119, 120	⊢
	: , :
116	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
117	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
118	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
119	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
120	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
*equality replacement requirements