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.ordering.transitivity_less_eq_less_eq
2	instantiation	4, 5, 6, 98, 86, 7, 8, 9*	⊢
	: , : , : , :
3	instantiation	10, 11, 12, 13	⊢
	: , :
4	theorem		⊢
	proveit.numbers.summation.integral_upper_bound_of_sum
5	theorem		⊢
	proveit.numbers.functions.one_over_x_sqrd_in_mon_dec_fxns
6	instantiation	100, 14	⊢
	: , :
7	instantiation	15, 105, 69, 46, 47, 41*	⊢
	: , : , :
8	instantiation	16, 17	⊢
	: , : , :
9	instantiation	48, 18, 19	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.integration.boundedInvSqrdIntegral
11	instantiation	129, 20, 21	⊢
	: , : , :
12	instantiation	34, 55, 22	⊢
	:
13	instantiation	23, 33	⊢
	: , :
14	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
15	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
16	theorem		⊢
	proveit.logic.sets.inclusion.fold_subset_eq
17	generalization	24	⊢
18	instantiation	59, 62, 131, 121, 64, 25, 28, 96, 26	⊢
	: , : , : , : , : , :
19	instantiation	27, 96, 28, 29	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
21	instantiation	129, 30, 31	⊢
	: , : , :
22	instantiation	32, 70, 33	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.ordering.relax_less
24	instantiation	34, 35, 36	,  ⊢
	:
25	instantiation	74	⊢
	: , :
26	instantiation	37, 96	⊢
	:
27	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_23
28	instantiation	129, 104, 69	⊢
	: , : , :
29	instantiation	38	⊢
	:
30	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
31	instantiation	39, 106, 70	⊢
	:
32	axiom		⊢
	proveit.numbers.ordering.transitivity_less_less
33	instantiation	82, 40, 41	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
35	instantiation	42, 54, 55, 56	,  ⊢
	: , : , :
36	instantiation	79, 43, 44	,  ⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.negation.complex_closure
38	axiom		⊢
	proveit.logic.equality.equals_reflexivity
39	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
40	instantiation	45, 69, 46, 105, 47, 80	⊢
	: , : , :
41	instantiation	48, 49, 50	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_cc__is__real
43	instantiation	51, 52	⊢
	: , :
44	instantiation	53, 54, 55, 56	,  ⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right_strong
46	instantiation	129, 111, 57	⊢
	: , : , :
47	instantiation	58, 119, 120, 114	⊢
	: , : , :
48	axiom		⊢
	proveit.logic.equality.equals_transitivity
49	instantiation	59, 62, 131, 121, 64, 60, 65, 92, 96	⊢
	: , : , : , : , : , :
50	instantiation	61, 121, 131, 62, 63, 64, 65, 92, 96, 66*	⊢
	: , : , : , : , : , :
51	theorem		⊢
	proveit.numbers.addition.subtraction.pos_difference
52	instantiation	67, 105, 68, 69, 70, 71*	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_cc_lower_bound
54	instantiation	129, 111, 72	⊢
	: , : , :
55	instantiation	129, 111, 73	⊢
	: , : , :
56	assumption		⊢
57	instantiation	129, 117, 120	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
59	theorem		⊢
	proveit.numbers.addition.disassociation
60	instantiation	74	⊢
	: , :
61	theorem		⊢
	proveit.numbers.addition.association
62	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
63	instantiation	74	⊢
	: , :
64	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
65	instantiation	129, 104, 75	⊢
	: , : , :
66	instantiation	82, 76, 77	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
68	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
69	instantiation	129, 111, 78	⊢
	: , : , :
70	instantiation	79, 80, 81	⊢
	: , : , :
71	instantiation	82, 83, 84	⊢
	: , : , :
72	instantiation	129, 117, 85	⊢
	: , : , :
73	instantiation	129, 117, 86	⊢
	: , : , :
74	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
75	instantiation	87, 88, 126	⊢
	: , : , :
76	instantiation	89, 96, 90, 91	⊢
	: , : , :
77	instantiation	95, 96, 92	⊢
	: , :
78	instantiation	129, 117, 106	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
80	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
81	instantiation	93, 119, 120, 114	⊢
	: , : , :
82	theorem		⊢
	proveit.logic.equality.sub_right_side_into
83	instantiation	94, 96	⊢
	:
84	instantiation	95, 96, 97	⊢
	: , :
85	instantiation	122, 98, 99	⊢
	: , :
86	instantiation	122, 123, 99	⊢
	: , :
87	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
88	instantiation	100, 101	⊢
	: , :
89	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add_reversed
90	instantiation	129, 104, 102	⊢
	: , : , :
91	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
92	instantiation	129, 104, 103	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
94	theorem		⊢
	proveit.numbers.addition.elim_zero_right
95	theorem		⊢
	proveit.numbers.addition.commutation
96	instantiation	129, 104, 105	⊢
	: , : , :
97	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
98	instantiation	122, 106, 119	⊢
	: , :
99	instantiation	129, 107, 108	⊢
	: , : , :
100	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
101	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
102	instantiation	129, 111, 109	⊢
	: , : , :
103	instantiation	129, 111, 110	⊢
	: , : , :
104	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
105	instantiation	129, 111, 112	⊢
	: , : , :
106	instantiation	129, 113, 114	⊢
	: , : , :
107	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
108	instantiation	115, 116	⊢
	:
109	instantiation	129, 117, 128	⊢
	: , : , :
110	instantiation	129, 117, 124	⊢
	: , : , :
111	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
112	instantiation	129, 117, 119	⊢
	: , : , :
113	instantiation	118, 119, 120	⊢
	: , :
114	assumption		⊢
115	theorem		⊢
	proveit.numbers.negation.int_neg_closure
116	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
117	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
118	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
119	instantiation	129, 130, 121	⊢
	: , : , :
120	instantiation	122, 123, 124	⊢
	: , :
121	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
122	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
123	instantiation	129, 125, 126	⊢
	: , : , :
124	instantiation	127, 128	⊢
	:
125	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
126	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
127	theorem		⊢
	proveit.numbers.negation.int_closure
128	instantiation	129, 130, 131	⊢
	: , : , :
129	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
130	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
131	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements