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	200, 184, 7	⊢
	: , : , :
3	instantiation	95, 10, 9	⊢
	: , :
4	instantiation	95, 11, 9	⊢
	: , :
5	instantiation	8, 9, 10, 11, 12	⊢
	: , : , :
6	instantiation	88, 13	⊢
	: , :
7	instantiation	200, 14, 24	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
9	modus ponens	15, 16	⊢
10	modus ponens	17, 18	⊢
11	modus ponens	19, 20	⊢
12	modus ponens	21, 22	⊢
13	instantiation	23, 24	⊢
	:
14	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
15	instantiation	27	⊢
	: , : , :
16	generalization	25	⊢
17	instantiation	27	⊢
	: , : , :
18	generalization	26	⊢
19	instantiation	27	⊢
	: , : , :
20	generalization	28	⊢
21	instantiation	29	⊢
	: , : , :
22	generalization	30	⊢
23	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
24	instantiation	31, 32, 33	⊢
	: , :
25	instantiation	38, 179, 34, 35	,  ⊢
	: , :
26	instantiation	38, 179, 36, 37	,  ⊢
	: , :
27	theorem		⊢
	proveit.numbers.summation.summation_real_closure
28	instantiation	38, 179, 39, 40	,  ⊢
	: , :
29	theorem		⊢
	proveit.numbers.summation.weak_summation_from_summands_bound
30	instantiation	41, 42, 59, 57, 43	,  ⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
32	instantiation	200, 44, 162	⊢
	: , : , :
33	instantiation	200, 44, 45	⊢
	: , : , :
34	instantiation	48, 84, 202	,  ⊢
	: , :
35	instantiation	49, 46	,  ⊢
	:
36	instantiation	48, 73, 202	,  ⊢
	: , :
37	instantiation	49, 47	,  ⊢
	:
38	theorem		⊢
	proveit.numbers.division.div_real_closure
39	instantiation	48, 94, 202	,  ⊢
	: , :
40	instantiation	49, 50	,  ⊢
	:
41	theorem		⊢
	proveit.numbers.division.weak_div_from_denom_bound__all_pos
42	instantiation	200, 51, 52	⊢
	: , : , :
43	instantiation	53, 150, 73, 94, 54, 55	,  ⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
45	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
46	instantiation	200, 58, 56	,  ⊢
	: , : , :
47	instantiation	200, 58, 57	,  ⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.exponentiation.exp_real_closure_nat_power
49	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
50	instantiation	200, 58, 59	,  ⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg
52	instantiation	200, 60, 195	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.exponentiation.exp_even_neg_base_lesseq
54	instantiation	61, 62, 100	,  ⊢
	: , :
55	instantiation	63	⊢
	:
56	instantiation	66, 84, 64	,  ⊢
	:
57	instantiation	66, 73, 65	,  ⊢
	:
58	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
59	instantiation	66, 94, 67	,  ⊢
	:
60	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg
61	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
62	instantiation	68, 94, 97, 144, 69, 70*	,  ⊢
	: , : , :
63	axiom		⊢
	proveit.logic.equality.equals_reflexivity
64	instantiation	71, 72	,  ⊢
	: , :
65	instantiation	83, 73, 144, 74	,  ⊢
	: , :
66	theorem		⊢
	proveit.numbers.exponentiation.sqrd_pos_closure
67	instantiation	75, 125, 76, 100	,  ⊢
	: , :
68	theorem		⊢
	proveit.numbers.addition.weak_bound_via_right_term_bound
69	instantiation	77, 78, 144, 110, 101, 79, 80*, 81*	⊢
	: , : , :
70	instantiation	169, 82	,  ⊢
	:
71	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
72	instantiation	83, 144, 84, 85	,  ⊢
	: , :
73	instantiation	95, 94, 97	,  ⊢
	: , :
74	instantiation	86, 87	,  ⊢
	: , :
75	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_int
76	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
77	theorem		⊢
	proveit.numbers.multiplication.reversed_weak_bound_via_right_factor_bound
78	instantiation	109, 179	⊢
	:
79	instantiation	88, 89	⊢
	: , :
80	instantiation	90, 91, 92	⊢
	: , : , :
81	instantiation	93, 104	⊢
	:
82	instantiation	200, 178, 94	,  ⊢
	: , : , :
83	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq
84	instantiation	95, 96, 97	,  ⊢
	: , :
85	instantiation	98, 99	,  ⊢
	: , :
86	theorem		⊢
	proveit.numbers.addition.subtraction.neg_difference
87	instantiation	180, 100, 101	,  ⊢
	: , : , :
88	theorem		⊢
	proveit.numbers.ordering.relax_less
89	instantiation	133, 102	⊢
	:
90	axiom		⊢
	proveit.logic.equality.equals_transitivity
91	instantiation	103, 195, 202, 120, 122, 121, 104, 123, 124	⊢
	: , : , : , : , : , :
92	instantiation	105, 120, 202, 121, 122, 171, 123, 124, 106*	⊢
	: , : , : , : , :
93	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
94	instantiation	200, 184, 107	,  ⊢
	: , : , :
95	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
96	instantiation	200, 184, 108	,  ⊢
	: , : , :
97	instantiation	109, 110	⊢
	:
98	theorem		⊢
	proveit.numbers.addition.subtraction.pos_difference
99	instantiation	111, 112, 113	,  ⊢
	: , : , :
100	instantiation	114, 115, 116	,  ⊢
	: , : , :
101	instantiation	117, 144, 179, 129	⊢
	: , : , :
102	instantiation	148, 162	⊢
	:
103	theorem		⊢
	proveit.numbers.multiplication.disassociation
104	instantiation	118, 171	⊢
	:
105	theorem		⊢
	proveit.numbers.multiplication.mult_neg_any
106	instantiation	119, 120, 202, 121, 122, 123, 124	⊢
	: , : , : , :
107	instantiation	200, 190, 125	,  ⊢
	: , : , :
108	instantiation	200, 190, 126	,  ⊢
	: , : , :
109	theorem		⊢
	proveit.numbers.negation.real_closure
110	instantiation	127, 144, 179, 129	⊢
	: , : , :
111	axiom		⊢
	proveit.numbers.ordering.transitivity_less_less
112	instantiation	128, 144, 179, 129	⊢
	: , : , :
113	instantiation	180, 130, 131	,  ⊢
	: , : , :
114	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less
115	instantiation	132, 154, 155, 141	,  ⊢
	: , : , :
116	instantiation	133, 134	⊢
	:
117	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
118	theorem		⊢
	proveit.numbers.negation.complex_closure
119	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
120	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
121	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
122	instantiation	135	⊢
	: , :
123	instantiation	136, 137, 138	⊢
	: , :
124	instantiation	200, 178, 139	⊢
	: , : , :
125	instantiation	200, 140, 141	,  ⊢
	: , : , :
126	instantiation	200, 142, 147	,  ⊢
	: , : , :
127	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
128	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
129	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval
130	instantiation	143, 179, 144, 145, 174, 146*	⊢
	: , : , :
131	instantiation	186, 168, 193, 147	,  ⊢
	: , : , :
132	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
133	theorem		⊢
	proveit.numbers.number_sets.integers.negative_if_in_neg_int
134	instantiation	148, 149	⊢
	:
135	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
136	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
137	instantiation	200, 178, 150	⊢
	: , : , :
138	instantiation	200, 178, 151	⊢
	: , : , :
139	instantiation	152, 153	⊢
	:
140	instantiation	188, 154, 155	⊢
	: , :
141	assumption		⊢
142	instantiation	188, 168, 193	⊢
	: , :
143	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
144	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
145	instantiation	200, 184, 156	⊢
	: , : , :
146	instantiation	157, 158, 159	⊢
	: , : , :
147	assumption		⊢
148	theorem		⊢
	proveit.numbers.negation.int_neg_closure
149	instantiation	160, 161, 162	⊢
	: , :
150	instantiation	200, 184, 163	⊢
	: , : , :
151	instantiation	164, 165, 166	⊢
	: , : , :
152	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
153	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
154	instantiation	192, 167, 191	⊢
	: , :
155	instantiation	198, 168	⊢
	:
156	instantiation	200, 190, 177	⊢
	: , : , :
157	theorem		⊢
	proveit.logic.equality.sub_right_side_into
158	instantiation	169, 171	⊢
	:
159	instantiation	170, 171, 172	⊢
	: , :
160	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
161	instantiation	173, 177, 174	⊢
	:
162	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
163	instantiation	200, 190, 199	⊢
	: , : , :
164	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
165	instantiation	175, 176	⊢
	: , :
166	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
167	instantiation	198, 193	⊢
	:
168	instantiation	192, 177, 191	⊢
	: , :
169	theorem		⊢
	proveit.numbers.addition.elim_zero_right
170	theorem		⊢
	proveit.numbers.addition.commutation
171	instantiation	200, 178, 179	⊢
	: , : , :
172	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
173	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
174	instantiation	180, 181, 182	⊢
	: , : , :
175	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
176	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
177	instantiation	200, 183, 187	⊢
	: , : , :
178	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
179	instantiation	200, 184, 185	⊢
	: , : , :
180	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
181	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
182	instantiation	186, 191, 189, 187	⊢
	: , : , :
183	instantiation	188, 191, 189	⊢
	: , :
184	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
185	instantiation	200, 190, 191	⊢
	: , : , :
186	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
187	assumption		⊢
188	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
189	instantiation	192, 193, 194	⊢
	: , :
190	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
191	instantiation	200, 201, 195	⊢
	: , : , :
192	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
193	instantiation	200, 196, 197	⊢
	: , : , :
194	instantiation	198, 199	⊢
	:
195	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
196	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
197	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
198	theorem		⊢
	proveit.numbers.negation.int_closure
199	instantiation	200, 201, 202	⊢
	: , : , :
200	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
201	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
202	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements