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, 5, 6*, 7*	⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
2	reference	40	⊢
3	reference	35	⊢
4	instantiation	8, 73, 10	⊢
	: , :
5	instantiation	9, 35, 73, 10, 11, 12	⊢
	: , : , :
6	instantiation	81, 13, 14	⊢
	: , : , :
7	instantiation	106, 15, 16	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
9	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right_strong
10	instantiation	127, 117, 17	⊢
	: , : , :
11	instantiation	18, 35, 19, 20	⊢
	: , : , :
12	instantiation	21, 32	⊢
	:
13	instantiation	22, 27	⊢
	:
14	instantiation	23, 27, 24	⊢
	: , :
15	instantiation	25, 63, 88, 129, 64, 26, 67, 29, 27	⊢
	: , : , : , : , : , :
16	instantiation	28, 29, 67, 30	⊢
	: , : , :
17	instantiation	127, 31, 32	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
19	instantiation	127, 117, 33	⊢
	: , : , :
20	instantiation	34, 35, 109, 72, 36, 37*, 38*, 39*	⊢
	: , : , : , :
21	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
22	theorem		⊢
	proveit.numbers.addition.elim_zero_right
23	theorem		⊢
	proveit.numbers.addition.commutation
24	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
25	theorem		⊢
	proveit.numbers.addition.disassociation
26	instantiation	71	⊢
	: , :
27	instantiation	127, 125, 40	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_23
29	instantiation	127, 125, 52	⊢
	: , : , :
30	instantiation	41	⊢
	:
31	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
32	instantiation	42, 43, 44	⊢
	: , :
33	instantiation	45, 118, 46, 78	⊢
	: , :
34	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rescale_interval_co_membership
35	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
36	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval
37	instantiation	84, 47, 48, 49	⊢
	: , : , : , :
38	instantiation	50, 66	⊢
	:
39	instantiation	121, 66	⊢
	:
40	instantiation	51, 52	⊢
	:
41	axiom		⊢
	proveit.logic.equality.equals_reflexivity
42	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
43	instantiation	127, 53, 119	⊢
	: , : , :
44	instantiation	127, 53, 70	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.division.div_rational_closure
46	instantiation	127, 123, 54	⊢
	: , : , :
47	instantiation	55, 129, 88, 63, 56, 64, 66, 122, 67	⊢
	: , : , : , : , : , :
48	instantiation	106, 57, 58	⊢
	: , : , :
49	instantiation	113, 67	⊢
	:
50	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
51	theorem		⊢
	proveit.numbers.negation.real_closure
52	instantiation	77, 109, 59, 60	⊢
	: , :
53	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
54	instantiation	127, 61, 132	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.multiplication.disassociation
56	instantiation	71	⊢
	: , :
57	instantiation	62, 63, 88, 129, 64, 65, 66, 122, 67	⊢
	: , : , : , : , : , :
58	instantiation	114, 68	⊢
	: , : , :
59	instantiation	127, 117, 69	⊢
	: , : , :
60	instantiation	89, 70	⊢
	:
61	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
62	theorem		⊢
	proveit.numbers.multiplication.association
63	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
64	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
65	instantiation	71	⊢
	: , :
66	instantiation	127, 125, 72	⊢
	: , : , :
67	instantiation	127, 125, 73	⊢
	: , : , :
68	instantiation	81, 74, 75	⊢
	: , : , :
69	instantiation	127, 123, 76	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
71	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
72	instantiation	77, 109, 126, 78	⊢
	: , :
73	instantiation	79, 80	⊢
	:
74	instantiation	81, 82, 83	⊢
	: , : , :
75	instantiation	84, 85, 86, 87	⊢
	: , : , : , :
76	instantiation	127, 128, 88	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.division.div_real_closure
78	instantiation	89, 132	⊢
	:
79	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
80	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
81	theorem		⊢
	proveit.logic.equality.sub_right_side_into
82	instantiation	90, 101, 91, 92	⊢
	: , : , : , : , :
83	instantiation	106, 93, 94	⊢
	: , : , :
84	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
85	instantiation	114, 95	⊢
	: , : , :
86	instantiation	114, 95	⊢
	: , : , :
87	instantiation	121, 101	⊢
	:
88	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
89	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
90	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_denom_left
91	instantiation	127, 97, 96	⊢
	: , : , :
92	instantiation	127, 97, 98	⊢
	: , : , :
93	instantiation	114, 99	⊢
	: , : , :
94	instantiation	114, 100	⊢
	: , : , :
95	instantiation	116, 101	⊢
	:
96	instantiation	127, 103, 102	⊢
	: , : , :
97	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
98	instantiation	127, 103, 104	⊢
	: , : , :
99	instantiation	114, 105	⊢
	: , : , :
100	instantiation	106, 107, 108	⊢
	: , : , :
101	instantiation	127, 125, 109	⊢
	: , : , :
102	instantiation	127, 111, 110	⊢
	: , : , :
103	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
104	instantiation	127, 111, 112	⊢
	: , : , :
105	instantiation	113, 122	⊢
	:
106	axiom		⊢
	proveit.logic.equality.equals_transitivity
107	instantiation	114, 115	⊢
	: , : , :
108	instantiation	116, 122	⊢
	:
109	instantiation	127, 117, 118	⊢
	: , : , :
110	instantiation	127, 120, 119	⊢
	: , : , :
111	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
112	instantiation	127, 120, 132	⊢
	: , : , :
113	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
114	axiom		⊢
	proveit.logic.equality.substitution
115	instantiation	121, 122	⊢
	:
116	theorem		⊢
	proveit.numbers.division.frac_one_denom
117	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
118	instantiation	127, 123, 124	⊢
	: , : , :
119	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
120	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
121	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
122	instantiation	127, 125, 126	⊢
	: , : , :
123	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
124	instantiation	127, 128, 129	⊢
	: , : , :
125	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
126	instantiation	130, 131, 132	⊢
	: , : , :
127	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
128	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
129	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
130	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
131	instantiation	133, 134	⊢
	: , :
132	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
133	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
134	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
*equality replacement requirements