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