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	modus ponens	1, 2	⊢
1	instantiation	3	⊢
	: , : , :
2	generalization	4	⊢
3	theorem		⊢
	proveit.numbers.summation.weak_summation_from_summands_bound
4	instantiation	5, 6, 7, 8, 9	,  ⊢
	: , : , :
5	theorem		⊢
	proveit.numbers.division.weak_div_from_denom_bound__all_pos
6	instantiation	128, 10, 11	⊢
	: , : , :
7	instantiation	13, 58, 12	,  ⊢
	:
8	instantiation	13, 22, 14	,  ⊢
	:
9	instantiation	15, 93, 22, 58, 16, 17	,  ⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg
11	instantiation	128, 18, 120	⊢
	: , : , :
12	instantiation	19, 78, 20, 34	,  ⊢
	: , :
13	theorem		⊢
	proveit.numbers.exponentiation.sqrd_pos_closure
14	instantiation	21, 22, 50, 23	,  ⊢
	: , :
15	theorem		⊢
	proveit.numbers.exponentiation.exp_even_neg_base_lesseq
16	instantiation	24, 25, 34	,  ⊢
	: , :
17	instantiation	26	⊢
	:
18	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg
19	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_int
20	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
21	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq
22	instantiation	27, 58, 31	,  ⊢
	: , :
23	instantiation	28, 29	,  ⊢
	: , :
24	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
25	instantiation	30, 58, 31, 50, 32, 33*	,  ⊢
	: , : , :
26	axiom		⊢
	proveit.logic.equality.equals_reflexivity
27	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
28	theorem		⊢
	proveit.numbers.addition.subtraction.neg_difference
29	instantiation	100, 34, 38	,  ⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.addition.weak_bound_via_right_term_bound
31	instantiation	47, 37	⊢
	:
32	instantiation	35, 36, 50, 37, 38, 39, 40*, 41*	⊢
	: , : , :
33	instantiation	42, 43	,  ⊢
	:
34	instantiation	44, 45, 46	,  ⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.multiplication.reversed_weak_bound_via_right_factor_bound
36	instantiation	47, 82	⊢
	:
37	instantiation	48, 50, 82, 51	⊢
	: , : , :
38	instantiation	49, 50, 82, 51	⊢
	: , : , :
39	instantiation	52, 53	⊢
	: , :
40	instantiation	54, 55, 56	⊢
	: , : , :
41	instantiation	57, 64	⊢
	:
42	theorem		⊢
	proveit.numbers.addition.elim_zero_right
43	instantiation	128, 94, 58	,  ⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less
45	instantiation	59, 98, 99, 89	,  ⊢
	: , : , :
46	instantiation	61, 60	⊢
	:
47	theorem		⊢
	proveit.numbers.negation.real_closure
48	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
49	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
50	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
51	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval
52	theorem		⊢
	proveit.numbers.ordering.relax_less
53	instantiation	61, 62	⊢
	:
54	axiom		⊢
	proveit.logic.equality.equals_transitivity
55	instantiation	63, 120, 130, 73, 75, 74, 64, 76, 77	⊢
	: , : , : , : , : , :
56	instantiation	65, 73, 130, 74, 75, 71, 76, 77, 66*	⊢
	: , : , : , : , :
57	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
58	instantiation	128, 103, 67	,  ⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
60	instantiation	69, 68	⊢
	:
61	theorem		⊢
	proveit.numbers.number_sets.integers.negative_if_in_neg_int
62	instantiation	69, 81	⊢
	:
63	theorem		⊢
	proveit.numbers.multiplication.disassociation
64	instantiation	70, 71	⊢
	:
65	theorem		⊢
	proveit.numbers.multiplication.mult_neg_any
66	instantiation	72, 73, 130, 74, 75, 76, 77	⊢
	: , : , : , :
67	instantiation	128, 111, 78	,  ⊢
	: , : , :
68	instantiation	79, 80, 81	⊢
	: , :
69	theorem		⊢
	proveit.numbers.negation.int_neg_closure
70	theorem		⊢
	proveit.numbers.negation.complex_closure
71	instantiation	128, 94, 82	⊢
	: , : , :
72	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
73	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
74	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
75	instantiation	83	⊢
	: , :
76	instantiation	84, 85, 86	⊢
	: , :
77	instantiation	128, 94, 87	⊢
	: , : , :
78	instantiation	128, 88, 89	,  ⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
80	instantiation	90, 114, 91	⊢
	:
81	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
82	instantiation	128, 103, 92	⊢
	: , : , :
83	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
84	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
85	instantiation	128, 94, 93	⊢
	: , : , :
86	instantiation	128, 94, 95	⊢
	: , : , :
87	instantiation	96, 97	⊢
	:
88	instantiation	117, 98, 99	⊢
	: , :
89	assumption		⊢
90	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
91	instantiation	100, 101, 102	⊢
	: , : , :
92	instantiation	128, 111, 118	⊢
	: , : , :
93	instantiation	128, 103, 104	⊢
	: , : , :
94	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
95	instantiation	105, 106, 107	⊢
	: , : , :
96	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
97	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
98	instantiation	121, 108, 118	⊢
	: , :
99	instantiation	126, 109	⊢
	:
100	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
101	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
102	instantiation	110, 118, 119, 116	⊢
	: , : , :
103	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
104	instantiation	128, 111, 127	⊢
	: , : , :
105	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
106	instantiation	112, 113	⊢
	: , :
107	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
108	instantiation	126, 122	⊢
	:
109	instantiation	121, 114, 118	⊢
	: , :
110	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
111	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
112	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
113	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
114	instantiation	128, 115, 116	⊢
	: , : , :
115	instantiation	117, 118, 119	⊢
	: , :
116	assumption		⊢
117	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
118	instantiation	128, 129, 120	⊢
	: , : , :
119	instantiation	121, 122, 123	⊢
	: , :
120	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
121	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
122	instantiation	128, 124, 125	⊢
	: , : , :
123	instantiation	126, 127	⊢
	:
124	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
125	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
126	theorem		⊢
	proveit.numbers.negation.int_closure
127	instantiation	128, 129, 130	⊢
	: , : , :
128	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
129	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
130	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements