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, 64, 6, 7, 8*, 9*	,  ⊢
	: , : , :
3	instantiation	10, 11, 12*	,  ⊢
	:
4	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
5	instantiation	13, 82, 14	,  ⊢
	: , :
6	instantiation	119, 87, 15	⊢
	: , : , :
7	instantiation	16, 64, 17, 71, 66, 102	,  ⊢
	: , : , :
8	instantiation	47, 18, 19	,  ⊢
	: , : , :
9	instantiation	47, 20, 21	,  ⊢
	: , : , :
10	theorem		⊢
	proveit.physics.quantum.QPE._modabs_in_full_domain_simp
11	instantiation	22, 95, 113, 83, 23	,  ⊢
	: , : , :
12	instantiation	24, 25	,  ⊢
	:
13	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
14	instantiation	26, 64	,  ⊢
	:
15	instantiation	119, 94, 27	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right_strong
17	instantiation	119, 87, 28	⊢
	: , : , :
18	instantiation	55, 111, 121, 56, 39, 57, 50, 73, 41	,  ⊢
	: , : , : , : , : , :
19	instantiation	29, 50, 73, 30	,  ⊢
	: , : , :
20	instantiation	45, 31	⊢
	: , : , :
21	instantiation	47, 32, 33	,  ⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.number_sets.integers.in_interval
23	instantiation	34, 35, 36	,  ⊢
	: , :
24	theorem		⊢
	proveit.numbers.absolute_value.abs_neg_elim
25	instantiation	43, 52	,  ⊢
	: , :
26	theorem		⊢
	proveit.numbers.negation.real_closure
27	instantiation	112, 96, 109	⊢
	: , :
28	instantiation	119, 94, 96	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
30	instantiation	74	⊢
	:
31	instantiation	47, 37, 38	⊢
	: , : , :
32	instantiation	55, 111, 121, 56, 39, 57, 62, 73, 41	,  ⊢
	: , : , : , : , : , :
33	instantiation	40, 73, 41, 42	,  ⊢
	: , : , :
34	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
35	instantiation	105, 95, 96, 90	,  ⊢
	: , : , :
36	instantiation	43, 44	,  ⊢
	: , :
37	instantiation	45, 46	⊢
	: , : , :
38	instantiation	47, 48, 49	⊢
	: , : , :
39	instantiation	69	⊢
	: , :
40	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_21
41	instantiation	72, 50	,  ⊢
	:
42	instantiation	74	⊢
	:
43	theorem		⊢
	proveit.numbers.ordering.relax_less
44	instantiation	51, 52, 53	,  ⊢
	: , : , :
45	axiom		⊢
	proveit.logic.equality.substitution
46	instantiation	54, 73, 61	⊢
	: , :
47	axiom		⊢
	proveit.logic.equality.equals_transitivity
48	instantiation	55, 56, 121, 111, 57, 58, 62, 59, 61	⊢
	: , : , : , : , : , :
49	instantiation	60, 61, 62, 63	⊢
	: , : , :
50	instantiation	119, 81, 64	,  ⊢
	: , : , :
51	axiom		⊢
	proveit.numbers.ordering.transitivity_less_less
52	instantiation	65, 66, 67	,  ⊢
	: , : , :
53	instantiation	68, 116	⊢
	:
54	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
55	theorem		⊢
	proveit.numbers.addition.disassociation
56	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
57	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
58	instantiation	69	⊢
	: , :
59	instantiation	119, 81, 70	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
61	instantiation	119, 81, 71	⊢
	: , : , :
62	instantiation	72, 73	⊢
	:
63	instantiation	74	⊢
	:
64	instantiation	119, 87, 75	,  ⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less
66	instantiation	76, 95, 96, 90	,  ⊢
	: , : , :
67	instantiation	77, 78	⊢
	:
68	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
69	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
70	instantiation	119, 87, 79	⊢
	: , : , :
71	instantiation	119, 87, 80	⊢
	: , : , :
72	theorem		⊢
	proveit.numbers.negation.complex_closure
73	instantiation	119, 81, 82	⊢
	: , : , :
74	axiom		⊢
	proveit.logic.equality.equals_reflexivity
75	instantiation	119, 94, 83	,  ⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
77	theorem		⊢
	proveit.numbers.number_sets.integers.negative_if_in_neg_int
78	instantiation	84, 85	⊢
	:
79	instantiation	119, 94, 86	⊢
	: , : , :
80	instantiation	119, 94, 109	⊢
	: , : , :
81	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
82	instantiation	119, 87, 88	⊢
	: , : , :
83	instantiation	119, 89, 90	,  ⊢
	: , : , :
84	theorem		⊢
	proveit.numbers.negation.int_neg_closure
85	instantiation	91, 92, 93	⊢
	: , :
86	instantiation	117, 109	⊢
	:
87	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
88	instantiation	119, 94, 104	⊢
	: , : , :
89	instantiation	108, 95, 96	⊢
	: , :
90	assumption		⊢
91	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
92	instantiation	97, 104, 98	⊢
	:
93	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
94	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
95	instantiation	112, 99, 109	⊢
	: , :
96	instantiation	117, 100	⊢
	:
97	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
98	instantiation	101, 102, 103	⊢
	: , : , :
99	instantiation	117, 113	⊢
	:
100	instantiation	112, 104, 109	⊢
	: , :
101	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
102	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
103	instantiation	105, 109, 110, 107	⊢
	: , : , :
104	instantiation	119, 106, 107	⊢
	: , : , :
105	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
106	instantiation	108, 109, 110	⊢
	: , :
107	assumption		⊢
108	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
109	instantiation	119, 120, 111	⊢
	: , : , :
110	instantiation	112, 113, 114	⊢
	: , :
111	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
112	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
113	instantiation	119, 115, 116	⊢
	: , : , :
114	instantiation	117, 118	⊢
	:
115	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
116	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
117	theorem		⊢
	proveit.numbers.negation.int_closure
118	instantiation	119, 120, 121	⊢
	: , : , :
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.nat2
*equality replacement requirements