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