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.numbers.modular.int_mod_elimination
2	reference	135	⊢
3	instantiation	4, 5, 6, 127, 7	⊢
	: , : , :
4	theorem		⊢
	proveit.numbers.number_sets.integers.in_interval
5	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
6	instantiation	8, 129, 45	⊢
	: , :
7	instantiation	9, 10, 11	⊢
	: , :
8	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
9	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
10	instantiation	69, 12, 26	⊢
	: , : , :
11	instantiation	69, 13, 26	⊢
	: , : , :
12	instantiation	14, 124, 37, 92, 15, 16, 17*	⊢
	: , : , :
13	instantiation	18, 19, 129, 45, 20, 21	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.multiplication.weak_bound_via_right_factor_bound
15	instantiation	22, 37, 101, 38	⊢
	: , : , :
16	instantiation	23, 29	⊢
	: , :
17	instantiation	24, 117	⊢
	:
18	theorem		⊢
	proveit.numbers.ordering.less_add_right_weak_int
19	instantiation	25, 127, 26	⊢
	: , : , :
20	instantiation	27, 124, 92, 101, 28, 29, 100*	⊢
	: , : , :
21	instantiation	30, 31, 32	⊢
	: , :
22	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
23	theorem		⊢
	proveit.numbers.ordering.relax_less
24	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
25	theorem		⊢
	proveit.logic.equality.sub_left_side_into
26	instantiation	33, 124, 92, 103, 34, 35*	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.multiplication.strong_bound_via_right_factor_bound
28	instantiation	36, 37, 101, 38	⊢
	: , : , :
29	instantiation	39, 135	⊢
	:
30	theorem		⊢
	proveit.numbers.ordering.relax_equal_to_less_eq
31	instantiation	133, 112, 40	⊢
	: , : , :
32	instantiation	93	⊢
	:
33	theorem		⊢
	proveit.numbers.multiplication.left_mult_eq_real
34	instantiation	41, 42	⊢
	: , :
35	instantiation	69, 43, 44	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
37	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
38	axiom		⊢
	proveit.physics.quantum.QPE._phase_in_interval
39	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
40	instantiation	133, 128, 45	⊢
	: , : , :
41	theorem		⊢
	proveit.logic.equality.equals_reversal
42	instantiation	46, 113, 57, 47, 58, 48*, 49*	⊢
	: , : , :
43	instantiation	69, 50, 51	⊢
	: , : , :
44	instantiation	52, 53, 54, 55	⊢
	: , : , : , :
45	instantiation	56, 118	⊢
	:
46	theorem		⊢
	proveit.numbers.addition.right_add_eq_rational
47	instantiation	69, 57, 58	⊢
	: , : , :
48	instantiation	59, 91	⊢
	:
49	instantiation	97, 60, 61	⊢
	: , : , :
50	instantiation	62, 86, 87, 63, 64	⊢
	: , : , : , : , :
51	instantiation	97, 65, 66	⊢
	: , : , :
52	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
53	instantiation	107, 67	⊢
	: , : , :
54	instantiation	107, 68	⊢
	: , : , :
55	instantiation	116, 87	⊢
	:
56	theorem		⊢
	proveit.numbers.negation.int_closure
57	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.zero_is_rational
58	instantiation	69, 70, 71	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.addition.elim_zero_left
60	instantiation	72, 73, 74, 126, 75, 76, 79, 77, 91	⊢
	: , : , : , : , : , :
61	instantiation	78, 91, 79, 80	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_numer_left
63	instantiation	133, 82, 81	⊢
	: , : , :
64	instantiation	133, 82, 83	⊢
	: , : , :
65	instantiation	107, 84	⊢
	: , : , :
66	instantiation	107, 85	⊢
	: , : , :
67	instantiation	109, 86	⊢
	:
68	instantiation	109, 87	⊢
	:
69	theorem		⊢
	proveit.logic.equality.sub_right_side_into
70	instantiation	88, 127	⊢
	:
71	assumption		⊢
72	theorem		⊢
	proveit.numbers.addition.disassociation
73	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
74	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
75	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
76	instantiation	89	⊢
	: , :
77	instantiation	90, 91	⊢
	:
78	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
79	instantiation	133, 123, 92	⊢
	: , : , :
80	instantiation	93	⊢
	:
81	instantiation	133, 95, 94	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
83	instantiation	133, 95, 96	⊢
	: , : , :
84	instantiation	97, 98, 99	⊢
	: , : , :
85	instantiation	107, 100	⊢
	: , : , :
86	instantiation	133, 123, 101	⊢
	: , : , :
87	instantiation	133, 123, 102	⊢
	: , : , :
88	axiom		⊢
	proveit.physics.quantum.QPE._delta_b_def
89	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
90	theorem		⊢
	proveit.numbers.negation.complex_closure
91	instantiation	133, 123, 103	⊢
	: , : , :
92	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
93	axiom		⊢
	proveit.logic.equality.equals_reflexivity
94	instantiation	133, 105, 104	⊢
	: , : , :
95	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
96	instantiation	133, 105, 106	⊢
	: , : , :
97	axiom		⊢
	proveit.logic.equality.equals_transitivity
98	instantiation	107, 108	⊢
	: , : , :
99	instantiation	109, 117	⊢
	:
100	instantiation	110, 117	⊢
	:
101	instantiation	133, 112, 111	⊢
	: , : , :
102	instantiation	133, 112, 120	⊢
	: , : , :
103	instantiation	133, 112, 113	⊢
	: , : , :
104	instantiation	133, 114, 135	⊢
	: , : , :
105	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
106	instantiation	133, 114, 115	⊢
	: , : , :
107	axiom		⊢
	proveit.logic.equality.substitution
108	instantiation	116, 117	⊢
	:
109	theorem		⊢
	proveit.numbers.division.frac_one_denom
110	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
111	instantiation	133, 128, 118	⊢
	: , : , :
112	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
113	instantiation	119, 120, 121, 122	⊢
	: , :
114	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
115	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
116	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
117	instantiation	133, 123, 124	⊢
	: , : , :
118	instantiation	133, 125, 126	⊢
	: , : , :
119	theorem		⊢
	proveit.numbers.division.div_rational_closure
120	instantiation	133, 128, 127	⊢
	: , : , :
121	instantiation	133, 128, 129	⊢
	: , : , :
122	instantiation	130, 135	⊢
	:
123	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
124	instantiation	131, 132, 135	⊢
	: , : , :
125	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
126	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
127	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int
128	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
129	instantiation	133, 134, 135	⊢
	: , : , :
130	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
131	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
132	instantiation	136, 137	⊢
	: , :
133	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
134	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
135	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
136	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
137	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
*equality replacement requirements