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	reference	50	⊢
2	instantiation	8, 6, 7	⊢
	: , :
3	instantiation	8, 10, 11	⊢
	: , :
4	instantiation	8, 10, 12	⊢
	: , :
5	instantiation	9, 10, 11, 12, 13, 14	⊢
	: , : , :
6	instantiation	189, 170, 15	⊢
	: , : , :
7	instantiation	46, 161, 16, 17	⊢
	: , :
8	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
9	theorem		⊢
	proveit.numbers.multiplication.weak_bound_via_right_factor_bound
10	instantiation	189, 170, 18	⊢
	: , : , :
11	modus ponens	19, 20	⊢
12	instantiation	46, 161, 123, 21	⊢
	: , :
13	instantiation	22, 23, 24	⊢
	: , : , :
14	instantiation	58, 25	⊢
	: , :
15	instantiation	189, 28, 26	⊢
	: , : , :
16	instantiation	63, 123, 191	⊢
	: , :
17	instantiation	65, 27, 67	⊢
	: , :
18	instantiation	189, 28, 43	⊢
	: , : , :
19	instantiation	29	⊢
	: , : , :
20	generalization	30	⊢
21	instantiation	31, 147	⊢
	:
22	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less_eq
23	instantiation	32, 33, 34, 152, 139, 35, 36, 37*	⊢
	: , : , : , :
24	instantiation	38, 39, 40, 41	⊢
	: , :
25	instantiation	42, 43	⊢
	:
26	instantiation	59, 60, 44	⊢
	: , :
27	instantiation	189, 79, 45	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
29	theorem		⊢
	proveit.numbers.summation.summation_real_closure
30	instantiation	46, 161, 47, 48	,  ⊢
	: , :
31	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
32	theorem		⊢
	proveit.numbers.summation.integral_upper_bound_of_sum
33	theorem		⊢
	proveit.numbers.functions.one_over_x_sqrd_in_mon_dec_fxns
34	instantiation	154, 49	⊢
	: , :
35	instantiation	50, 161, 123, 95, 96, 87*	⊢
	: , : , :
36	instantiation	51, 52	⊢
	: , : , :
37	instantiation	97, 53, 54	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.integration.boundedInvSqrdIntegral
39	instantiation	189, 55, 56	⊢
	: , : , :
40	instantiation	81, 106, 57	⊢
	:
41	instantiation	58, 75	⊢
	: , :
42	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
43	instantiation	59, 60, 61	⊢
	: , :
44	instantiation	189, 76, 62	⊢
	: , : , :
45	instantiation	189, 89, 147	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.division.div_real_closure
47	instantiation	63, 64, 191	,  ⊢
	: , :
48	instantiation	65, 66, 67	,  ⊢
	: , :
49	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
50	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
51	theorem		⊢
	proveit.logic.sets.inclusion.fold_subset_eq
52	generalization	68	⊢
53	instantiation	110, 113, 191, 181, 115, 69, 72, 150, 70	⊢
	: , : , : , : , : , :
54	instantiation	71, 150, 72, 73	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
56	instantiation	189, 76, 147	⊢
	: , : , :
57	instantiation	74, 159, 75	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.ordering.relax_less
59	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
60	instantiation	189, 76, 174	⊢
	: , : , :
61	instantiation	189, 76, 90	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
63	theorem		⊢
	proveit.numbers.exponentiation.exp_real_closure_nat_power
64	instantiation	189, 170, 77	,  ⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
66	instantiation	189, 79, 78	,  ⊢
	: , : , :
67	instantiation	189, 79, 80	⊢
	: , : , :
68	instantiation	81, 82, 83	,  ⊢
	:
69	instantiation	127	⊢
	: , :
70	instantiation	84, 150	⊢
	:
71	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_23
72	instantiation	189, 160, 123	⊢
	: , : , :
73	instantiation	85	⊢
	:
74	axiom		⊢
	proveit.numbers.ordering.transitivity_less_less
75	instantiation	135, 86, 87	⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
77	instantiation	189, 177, 100	,  ⊢
	: , : , :
78	instantiation	189, 89, 88	,  ⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
80	instantiation	189, 89, 90	⊢
	: , : , :
81	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
82	instantiation	91, 105, 106, 107	,  ⊢
	: , : , :
83	instantiation	167, 92, 93	,  ⊢
	: , : , :
84	theorem		⊢
	proveit.numbers.negation.complex_closure
85	axiom		⊢
	proveit.logic.equality.equals_reflexivity
86	instantiation	94, 123, 95, 161, 96, 168	⊢
	: , : , :
87	instantiation	97, 98, 99	⊢
	: , : , :
88	instantiation	158, 100, 101	,  ⊢
	:
89	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
90	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
91	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_cc__is__real
92	instantiation	102, 103	⊢
	: , :
93	instantiation	104, 105, 106, 107	,  ⊢
	: , : , :
94	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right_strong
95	instantiation	189, 170, 108	⊢
	: , : , :
96	instantiation	109, 179, 180, 176	⊢
	: , : , :
97	axiom		⊢
	proveit.logic.equality.equals_transitivity
98	instantiation	110, 113, 191, 181, 115, 111, 116, 145, 150	⊢
	: , : , : , : , : , :
99	instantiation	112, 181, 191, 113, 114, 115, 116, 145, 150, 117*	⊢
	: , : , : , : , : , :
100	instantiation	189, 118, 133	,  ⊢
	: , : , :
101	instantiation	167, 119, 120	,  ⊢
	: , : , :
102	theorem		⊢
	proveit.numbers.addition.subtraction.pos_difference
103	instantiation	121, 161, 122, 123, 159, 124*	⊢
	: , : , :
104	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_cc_lower_bound
105	instantiation	189, 170, 125	⊢
	: , : , :
106	instantiation	189, 170, 126	⊢
	: , : , :
107	assumption		⊢
108	instantiation	189, 177, 180	⊢
	: , : , :
109	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
110	theorem		⊢
	proveit.numbers.addition.disassociation
111	instantiation	127	⊢
	: , :
112	theorem		⊢
	proveit.numbers.addition.association
113	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
114	instantiation	127	⊢
	: , :
115	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
116	instantiation	189, 160, 128	⊢
	: , : , :
117	instantiation	135, 129, 130	⊢
	: , : , :
118	instantiation	178, 152, 139	⊢
	: , :
119	instantiation	131, 132	⊢
	:
120	instantiation	175, 152, 139, 133	,  ⊢
	: , : , :
121	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
122	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
123	instantiation	189, 170, 134	⊢
	: , : , :
124	instantiation	135, 136, 137	⊢
	: , : , :
125	instantiation	189, 177, 138	⊢
	: , : , :
126	instantiation	189, 177, 139	⊢
	: , : , :
127	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
128	instantiation	140, 141, 186	⊢
	: , : , :
129	instantiation	142, 150, 143, 144	⊢
	: , : , :
130	instantiation	149, 150, 145	⊢
	: , :
131	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
132	instantiation	146, 147, 174	⊢
	: , :
133	assumption		⊢
134	instantiation	189, 177, 162	⊢
	: , : , :
135	theorem		⊢
	proveit.logic.equality.sub_right_side_into
136	instantiation	148, 150	⊢
	:
137	instantiation	149, 150, 151	⊢
	: , :
138	instantiation	182, 152, 153	⊢
	: , :
139	instantiation	182, 183, 153	⊢
	: , :
140	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
141	instantiation	154, 155	⊢
	: , :
142	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add_reversed
143	instantiation	189, 160, 156	⊢
	: , : , :
144	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
145	instantiation	189, 160, 157	⊢
	: , : , :
146	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
147	instantiation	158, 162, 159	⊢
	:
148	theorem		⊢
	proveit.numbers.addition.elim_zero_right
149	theorem		⊢
	proveit.numbers.addition.commutation
150	instantiation	189, 160, 161	⊢
	: , : , :
151	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
152	instantiation	182, 162, 179	⊢
	: , :
153	instantiation	189, 163, 164	⊢
	: , : , :
154	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
155	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
156	instantiation	189, 170, 165	⊢
	: , : , :
157	instantiation	189, 170, 166	⊢
	: , : , :
158	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
159	instantiation	167, 168, 169	⊢
	: , : , :
160	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
161	instantiation	189, 170, 171	⊢
	: , : , :
162	instantiation	189, 172, 176	⊢
	: , : , :
163	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
164	instantiation	173, 174	⊢
	:
165	instantiation	189, 177, 188	⊢
	: , : , :
166	instantiation	189, 177, 184	⊢
	: , : , :
167	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
168	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
169	instantiation	175, 179, 180, 176	⊢
	: , : , :
170	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
171	instantiation	189, 177, 179	⊢
	: , : , :
172	instantiation	178, 179, 180	⊢
	: , :
173	theorem		⊢
	proveit.numbers.negation.int_neg_closure
174	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
175	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
176	assumption		⊢
177	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
178	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
179	instantiation	189, 190, 181	⊢
	: , : , :
180	instantiation	182, 183, 184	⊢
	: , :
181	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
182	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
183	instantiation	189, 185, 186	⊢
	: , : , :
184	instantiation	187, 188	⊢
	:
185	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
186	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
187	theorem		⊢
	proveit.numbers.negation.int_closure
188	instantiation	189, 190, 191	⊢
	: , : , :
189	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
190	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
191	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements