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	,  ⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.division.weak_div_from_denom_bound__all_pos
2	instantiation	124, 6, 7	⊢
	: , : , :
3	instantiation	9, 54, 8	,  ⊢
	:
4	instantiation	9, 18, 10	,  ⊢
	:
5	instantiation	11, 89, 18, 54, 12, 13	,  ⊢
	: , : , :
6	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg
7	instantiation	124, 14, 116	⊢
	: , : , :
8	instantiation	15, 74, 16, 30	,  ⊢
	: , :
9	theorem		⊢
	proveit.numbers.exponentiation.sqrd_pos_closure
10	instantiation	17, 18, 46, 19	,  ⊢
	: , :
11	theorem		⊢
	proveit.numbers.exponentiation.exp_even_neg_base_lesseq
12	instantiation	20, 21, 30	,  ⊢
	: , :
13	instantiation	22	⊢
	:
14	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg
15	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_int
16	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
17	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq
18	instantiation	23, 54, 27	,  ⊢
	: , :
19	instantiation	24, 25	,  ⊢
	: , :
20	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
21	instantiation	26, 54, 27, 46, 28, 29*	,  ⊢
	: , : , :
22	axiom		⊢
	proveit.logic.equality.equals_reflexivity
23	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
24	theorem		⊢
	proveit.numbers.addition.subtraction.neg_difference
25	instantiation	96, 30, 34	,  ⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.addition.weak_bound_via_right_term_bound
27	instantiation	43, 33	⊢
	:
28	instantiation	31, 32, 46, 33, 34, 35, 36*, 37*	⊢
	: , : , :
29	instantiation	38, 39	,  ⊢
	:
30	instantiation	40, 41, 42	,  ⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.multiplication.reversed_weak_bound_via_right_factor_bound
32	instantiation	43, 78	⊢
	:
33	instantiation	44, 46, 78, 47	⊢
	: , : , :
34	instantiation	45, 46, 78, 47	⊢
	: , : , :
35	instantiation	48, 49	⊢
	: , :
36	instantiation	50, 51, 52	⊢
	: , : , :
37	instantiation	53, 60	⊢
	:
38	theorem		⊢
	proveit.numbers.addition.elim_zero_right
39	instantiation	124, 90, 54	,  ⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less
41	instantiation	55, 94, 95, 85	,  ⊢
	: , : , :
42	instantiation	57, 56	⊢
	:
43	theorem		⊢
	proveit.numbers.negation.real_closure
44	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
45	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
46	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
47	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval
48	theorem		⊢
	proveit.numbers.ordering.relax_less
49	instantiation	57, 58	⊢
	:
50	axiom		⊢
	proveit.logic.equality.equals_transitivity
51	instantiation	59, 116, 126, 69, 71, 70, 60, 72, 73	⊢
	: , : , : , : , : , :
52	instantiation	61, 69, 126, 70, 71, 67, 72, 73, 62*	⊢
	: , : , : , : , :
53	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
54	instantiation	124, 99, 63	,  ⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
56	instantiation	65, 64	⊢
	:
57	theorem		⊢
	proveit.numbers.number_sets.integers.negative_if_in_neg_int
58	instantiation	65, 77	⊢
	:
59	theorem		⊢
	proveit.numbers.multiplication.disassociation
60	instantiation	66, 67	⊢
	:
61	theorem		⊢
	proveit.numbers.multiplication.mult_neg_any
62	instantiation	68, 69, 126, 70, 71, 72, 73	⊢
	: , : , : , :
63	instantiation	124, 107, 74	,  ⊢
	: , : , :
64	instantiation	75, 76, 77	⊢
	: , :
65	theorem		⊢
	proveit.numbers.negation.int_neg_closure
66	theorem		⊢
	proveit.numbers.negation.complex_closure
67	instantiation	124, 90, 78	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
69	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
70	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
71	instantiation	79	⊢
	: , :
72	instantiation	80, 81, 82	⊢
	: , :
73	instantiation	124, 90, 83	⊢
	: , : , :
74	instantiation	124, 84, 85	,  ⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
76	instantiation	86, 110, 87	⊢
	:
77	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
78	instantiation	124, 99, 88	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
80	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
81	instantiation	124, 90, 89	⊢
	: , : , :
82	instantiation	124, 90, 91	⊢
	: , : , :
83	instantiation	92, 93	⊢
	:
84	instantiation	113, 94, 95	⊢
	: , :
85	assumption		⊢
86	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
87	instantiation	96, 97, 98	⊢
	: , : , :
88	instantiation	124, 107, 114	⊢
	: , : , :
89	instantiation	124, 99, 100	⊢
	: , : , :
90	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
91	instantiation	101, 102, 103	⊢
	: , : , :
92	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
93	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
94	instantiation	117, 104, 114	⊢
	: , :
95	instantiation	122, 105	⊢
	:
96	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
97	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
98	instantiation	106, 114, 115, 112	⊢
	: , : , :
99	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
100	instantiation	124, 107, 123	⊢
	: , : , :
101	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
102	instantiation	108, 109	⊢
	: , :
103	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
104	instantiation	122, 118	⊢
	:
105	instantiation	117, 110, 114	⊢
	: , :
106	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
107	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
108	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
109	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
110	instantiation	124, 111, 112	⊢
	: , : , :
111	instantiation	113, 114, 115	⊢
	: , :
112	assumption		⊢
113	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
114	instantiation	124, 125, 116	⊢
	: , : , :
115	instantiation	117, 118, 119	⊢
	: , :
116	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
117	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
118	instantiation	124, 120, 121	⊢
	: , : , :
119	instantiation	122, 123	⊢
	:
120	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
121	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
122	theorem		⊢
	proveit.numbers.negation.int_closure
123	instantiation	124, 125, 126	⊢
	: , : , :
124	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
125	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
126	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements