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	⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.multiplication.weak_bound_via_right_factor_bound
2	instantiation	173, 154, 7	⊢
	: , : , :
3	modus ponens	8, 9	⊢
4	instantiation	31, 145, 107, 10	⊢
	: , :
5	instantiation	11, 12, 13	⊢
	: , : , :
6	instantiation	43, 14	⊢
	: , :
7	instantiation	173, 15, 30	⊢
	: , : , :
8	instantiation	16	⊢
	: , : , :
9	generalization	17	⊢
10	instantiation	18, 131	⊢
	:
11	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less_eq
12	instantiation	19, 20, 21, 136, 123, 22, 23, 24*	⊢
	: , : , : , :
13	instantiation	25, 26, 27, 28	⊢
	: , :
14	instantiation	29, 30	⊢
	:
15	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
16	theorem		⊢
	proveit.numbers.summation.summation_real_closure
17	instantiation	31, 145, 32, 33	,  ⊢
	: , :
18	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
19	theorem		⊢
	proveit.numbers.summation.integral_upper_bound_of_sum
20	theorem		⊢
	proveit.numbers.functions.one_over_x_sqrd_in_mon_dec_fxns
21	instantiation	138, 34	⊢
	: , :
22	instantiation	35, 145, 107, 79, 80, 71*	⊢
	: , : , :
23	instantiation	36, 37	⊢
	: , : , :
24	instantiation	81, 38, 39	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.integration.boundedInvSqrdIntegral
26	instantiation	173, 40, 41	⊢
	: , : , :
27	instantiation	65, 90, 42	⊢
	:
28	instantiation	43, 59	⊢
	: , :
29	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
30	instantiation	44, 45, 46	⊢
	: , :
31	theorem		⊢
	proveit.numbers.division.div_real_closure
32	instantiation	47, 48, 175	,  ⊢
	: , :
33	instantiation	49, 50, 51	,  ⊢
	: , :
34	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
35	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
36	theorem		⊢
	proveit.logic.sets.inclusion.fold_subset_eq
37	generalization	52	⊢
38	instantiation	94, 97, 175, 165, 99, 53, 56, 134, 54	⊢
	: , : , : , : , : , :
39	instantiation	55, 134, 56, 57	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
41	instantiation	173, 60, 131	⊢
	: , : , :
42	instantiation	58, 143, 59	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.ordering.relax_less
44	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
45	instantiation	173, 60, 158	⊢
	: , : , :
46	instantiation	173, 60, 74	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.exponentiation.exp_real_closure_nat_power
48	instantiation	173, 154, 61	,  ⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
50	instantiation	173, 63, 62	,  ⊢
	: , : , :
51	instantiation	173, 63, 64	⊢
	: , : , :
52	instantiation	65, 66, 67	,  ⊢
	:
53	instantiation	111	⊢
	: , :
54	instantiation	68, 134	⊢
	:
55	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_23
56	instantiation	173, 144, 107	⊢
	: , : , :
57	instantiation	69	⊢
	:
58	axiom		⊢
	proveit.numbers.ordering.transitivity_less_less
59	instantiation	119, 70, 71	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
61	instantiation	173, 161, 84	,  ⊢
	: , : , :
62	instantiation	173, 73, 72	,  ⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
64	instantiation	173, 73, 74	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
66	instantiation	75, 89, 90, 91	,  ⊢
	: , : , :
67	instantiation	151, 76, 77	,  ⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.negation.complex_closure
69	axiom		⊢
	proveit.logic.equality.equals_reflexivity
70	instantiation	78, 107, 79, 145, 80, 152	⊢
	: , : , :
71	instantiation	81, 82, 83	⊢
	: , : , :
72	instantiation	142, 84, 85	,  ⊢
	:
73	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
74	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
75	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_cc__is__real
76	instantiation	86, 87	⊢
	: , :
77	instantiation	88, 89, 90, 91	,  ⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right_strong
79	instantiation	173, 154, 92	⊢
	: , : , :
80	instantiation	93, 163, 164, 160	⊢
	: , : , :
81	axiom		⊢
	proveit.logic.equality.equals_transitivity
82	instantiation	94, 97, 175, 165, 99, 95, 100, 129, 134	⊢
	: , : , : , : , : , :
83	instantiation	96, 165, 175, 97, 98, 99, 100, 129, 134, 101*	⊢
	: , : , : , : , : , :
84	instantiation	173, 102, 117	,  ⊢
	: , : , :
85	instantiation	151, 103, 104	,  ⊢
	: , : , :
86	theorem		⊢
	proveit.numbers.addition.subtraction.pos_difference
87	instantiation	105, 145, 106, 107, 143, 108*	⊢
	: , : , :
88	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_cc_lower_bound
89	instantiation	173, 154, 109	⊢
	: , : , :
90	instantiation	173, 154, 110	⊢
	: , : , :
91	assumption		⊢
92	instantiation	173, 161, 164	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
94	theorem		⊢
	proveit.numbers.addition.disassociation
95	instantiation	111	⊢
	: , :
96	theorem		⊢
	proveit.numbers.addition.association
97	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
98	instantiation	111	⊢
	: , :
99	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
100	instantiation	173, 144, 112	⊢
	: , : , :
101	instantiation	119, 113, 114	⊢
	: , : , :
102	instantiation	162, 136, 123	⊢
	: , :
103	instantiation	115, 116	⊢
	:
104	instantiation	159, 136, 123, 117	,  ⊢
	: , : , :
105	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
106	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
107	instantiation	173, 154, 118	⊢
	: , : , :
108	instantiation	119, 120, 121	⊢
	: , : , :
109	instantiation	173, 161, 122	⊢
	: , : , :
110	instantiation	173, 161, 123	⊢
	: , : , :
111	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
112	instantiation	124, 125, 170	⊢
	: , : , :
113	instantiation	126, 134, 127, 128	⊢
	: , : , :
114	instantiation	133, 134, 129	⊢
	: , :
115	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
116	instantiation	130, 131, 158	⊢
	: , :
117	assumption		⊢
118	instantiation	173, 161, 146	⊢
	: , : , :
119	theorem		⊢
	proveit.logic.equality.sub_right_side_into
120	instantiation	132, 134	⊢
	:
121	instantiation	133, 134, 135	⊢
	: , :
122	instantiation	166, 136, 137	⊢
	: , :
123	instantiation	166, 167, 137	⊢
	: , :
124	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
125	instantiation	138, 139	⊢
	: , :
126	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add_reversed
127	instantiation	173, 144, 140	⊢
	: , : , :
128	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
129	instantiation	173, 144, 141	⊢
	: , : , :
130	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
131	instantiation	142, 146, 143	⊢
	:
132	theorem		⊢
	proveit.numbers.addition.elim_zero_right
133	theorem		⊢
	proveit.numbers.addition.commutation
134	instantiation	173, 144, 145	⊢
	: , : , :
135	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
136	instantiation	166, 146, 163	⊢
	: , :
137	instantiation	173, 147, 148	⊢
	: , : , :
138	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
139	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
140	instantiation	173, 154, 149	⊢
	: , : , :
141	instantiation	173, 154, 150	⊢
	: , : , :
142	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
143	instantiation	151, 152, 153	⊢
	: , : , :
144	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
145	instantiation	173, 154, 155	⊢
	: , : , :
146	instantiation	173, 156, 160	⊢
	: , : , :
147	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
148	instantiation	157, 158	⊢
	:
149	instantiation	173, 161, 172	⊢
	: , : , :
150	instantiation	173, 161, 168	⊢
	: , : , :
151	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
152	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
153	instantiation	159, 163, 164, 160	⊢
	: , : , :
154	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
155	instantiation	173, 161, 163	⊢
	: , : , :
156	instantiation	162, 163, 164	⊢
	: , :
157	theorem		⊢
	proveit.numbers.negation.int_neg_closure
158	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
159	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
160	assumption		⊢
161	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
162	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
163	instantiation	173, 174, 165	⊢
	: , : , :
164	instantiation	166, 167, 168	⊢
	: , :
165	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
166	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
167	instantiation	173, 169, 170	⊢
	: , : , :
168	instantiation	171, 172	⊢
	:
169	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
170	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
171	theorem		⊢
	proveit.numbers.negation.int_closure
172	instantiation	173, 174, 175	⊢
	: , : , :
173	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
174	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
175	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements