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	axiom		⊢
	proveit.numbers.ordering.transitivity_less_less
2	instantiation	41, 4, 22	⊢
	: , : , :
3	instantiation	52, 50, 5, 6, 7*, 8*	⊢
	: , : , :
4	instantiation	9, 10, 11	⊢
	: , : , :
5	instantiation	69, 70, 13	⊢
	: , :
6	instantiation	12, 70, 13, 81, 44, 14	⊢
	: , : , :
7	instantiation	142, 15, 16	⊢
	: , : , :
8	instantiation	17, 18, 19*	⊢
	: , :
9	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
10	instantiation	20, 21, 22	⊢
	: , : , :
11	instantiation	23, 81, 24, 137, 25, 26, 27*, 28*	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.multiplication.strong_bound_via_right_factor_bound
13	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
14	instantiation	29, 119	⊢
	:
15	instantiation	83, 30	⊢
	: , : , :
16	instantiation	31, 32	⊢
	:
17	theorem		⊢
	proveit.logic.equality.equals_reversal
18	instantiation	33, 100, 194, 187, 101, 34, 49, 58	⊢
	: , : , : , : , : , :
19	instantiation	142, 35, 36	⊢
	: , : , :
20	theorem		⊢
	proveit.logic.equality.sub_left_side_into
21	instantiation	37, 187, 107, 109, 38, 39*	⊢
	: , : , : , : , : , :
22	instantiation	83, 40	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.multiplication.weak_bound_via_right_factor_bound
24	instantiation	69, 132, 82	⊢
	: , :
25	instantiation	41, 42, 43	⊢
	: , : , :
26	instantiation	116, 44	⊢
	: , :
27	instantiation	45, 187, 194, 100, 46, 101, 58, 105, 59	⊢
	: , : , : , : , : , :
28	instantiation	47, 58, 49	⊢
	: , :
29	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
30	instantiation	48, 49	⊢
	:
31	theorem		⊢
	proveit.numbers.addition.elim_zero_left
32	instantiation	192, 184, 50	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
34	instantiation	175	⊢
	: , :
35	instantiation	83, 51	⊢
	: , : , :
36	instantiation	176, 58	⊢
	:
37	theorem		⊢
	proveit.numbers.multiplication.strong_bound_via_factor_bound
38	instantiation	52, 131, 185, 53, 54, 55*, 56*	⊢
	: , : , :
39	instantiation	57, 187, 58, 59	⊢
	: , : , : , :
40	instantiation	142, 60, 61	⊢
	: , : , :
41	theorem		⊢
	proveit.logic.equality.sub_right_side_into
42	instantiation	62, 63, 64	⊢
	: , :
43	instantiation	65, 174, 66, 105, 153, 67*	⊢
	: , :
44	instantiation	68, 107	⊢
	:
45	theorem		⊢
	proveit.numbers.multiplication.disassociation
46	instantiation	175	⊢
	: , :
47	theorem		⊢
	proveit.numbers.multiplication.commutation
48	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
49	instantiation	192, 184, 137	⊢
	: , : , :
50	instantiation	69, 70, 81	⊢
	: , :
51	instantiation	71, 183, 191, 72*	⊢
	: , : , : , :
52	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
53	instantiation	192, 188, 73	⊢
	: , : , :
54	instantiation	74, 185, 132, 156, 75, 76	⊢
	: , : , :
55	instantiation	77, 111, 178, 78	⊢
	: , : , :
56	instantiation	142, 79, 80	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
58	instantiation	192, 184, 81	⊢
	: , : , :
59	instantiation	192, 184, 82	⊢
	: , : , :
60	instantiation	83, 84	⊢
	: , : , :
61	instantiation	85, 153	⊢
	:
62	theorem		⊢
	proveit.numbers.absolute_value.weak_upper_bound
63	instantiation	86, 114, 137, 115	⊢
	: , : , :
64	instantiation	116, 87	⊢
	: , :
65	theorem		⊢
	proveit.numbers.absolute_value.abs_prod
66	instantiation	175	⊢
	: , :
67	instantiation	88, 89	⊢
	:
68	theorem		⊢
	proveit.numbers.number_sets.real_numbers.positive_if_in_real_pos
69	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
70	instantiation	192, 188, 90	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
72	instantiation	142, 91, 92	⊢
	: , : , :
73	instantiation	192, 190, 93	⊢
	: , : , :
74	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right_strong
75	instantiation	94, 185, 156, 95, 96, 97, 98*	⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
77	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
78	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
79	instantiation	99, 100, 194, 187, 101, 102, 105, 111, 103	⊢
	: , : , : , : , : , :
80	instantiation	104, 111, 105, 106	⊢
	: , : , :
81	instantiation	192, 108, 107	⊢
	: , : , :
82	instantiation	192, 108, 109	⊢
	: , : , :
83	axiom		⊢
	proveit.logic.equality.substitution
84	instantiation	110, 111, 153, 112*	⊢
	: , :
85	theorem		⊢
	proveit.numbers.absolute_value.abs_even
86	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
87	instantiation	113, 114, 137, 115	⊢
	: , : , :
88	theorem		⊢
	proveit.numbers.absolute_value.abs_non_neg_elim
89	instantiation	116, 117	⊢
	: , :
90	instantiation	192, 118, 119	⊢
	: , : , :
91	instantiation	160, 194, 120, 121, 122, 123	⊢
	: , : , : , :
92	instantiation	124, 125, 126	⊢
	:
93	instantiation	192, 193, 127	⊢
	: , : , :
94	theorem		⊢
	proveit.numbers.exponentiation.exp_monotonicity_large_base_less_eq
95	instantiation	150, 151, 129	⊢
	: , : , :
96	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
97	instantiation	128, 129	⊢
	:
98	instantiation	130, 178	⊢
	:
99	theorem		⊢
	proveit.numbers.addition.disassociation
100	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
101	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
102	instantiation	175	⊢
	: , :
103	instantiation	192, 184, 131	⊢
	: , : , :
104	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_23
105	instantiation	192, 184, 132	⊢
	: , : , :
106	instantiation	133	⊢
	:
107	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
108	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
109	instantiation	134, 135	⊢
	:
110	theorem		⊢
	proveit.numbers.multiplication.mult_neg_left
111	instantiation	192, 184, 156	⊢
	: , : , :
112	instantiation	176, 153	⊢
	:
113	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
114	instantiation	136, 137	⊢
	:
115	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_round_in_interval
116	theorem		⊢
	proveit.numbers.ordering.relax_less
117	instantiation	138, 167	⊢
	:
118	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
119	instantiation	139, 140, 141	⊢
	: , :
120	instantiation	175	⊢
	: , :
121	instantiation	175	⊢
	: , :
122	instantiation	142, 143, 144	⊢
	: , : , :
123	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
124	theorem		⊢
	proveit.numbers.division.frac_cancel_complete
125	instantiation	192, 184, 145	⊢
	: , : , :
126	instantiation	173, 146	⊢
	:
127	instantiation	147, 148, 187	⊢
	: , :
128	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
129	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
130	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
131	instantiation	192, 188, 149	⊢
	: , : , :
132	instantiation	150, 151, 167	⊢
	: , : , :
133	axiom		⊢
	proveit.logic.equality.equals_reflexivity
134	theorem		⊢
	proveit.numbers.absolute_value.abs_nonzero_closure
135	instantiation	152, 153, 154	⊢
	:
136	theorem		⊢
	proveit.numbers.negation.real_closure
137	instantiation	155, 156, 185, 157	⊢
	: , :
138	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
139	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
140	instantiation	192, 159, 158	⊢
	: , : , :
141	instantiation	192, 159, 174	⊢
	: , : , :
142	axiom		⊢
	proveit.logic.equality.equals_transitivity
143	instantiation	160, 194, 161, 162, 163, 164	⊢
	: , : , : , :
144	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
145	instantiation	192, 188, 165	⊢
	: , : , :
146	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
147	theorem		⊢
	proveit.numbers.addition.add_nat_closure_bin
148	instantiation	192, 166, 167	⊢
	: , : , :
149	instantiation	192, 190, 168	⊢
	: , : , :
150	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
151	instantiation	169, 170	⊢
	: , :
152	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
153	instantiation	192, 184, 171	⊢
	: , : , :
154	assumption		⊢
155	theorem		⊢
	proveit.numbers.division.div_real_closure
156	instantiation	192, 188, 172	⊢
	: , : , :
157	instantiation	173, 174	⊢
	:
158	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
159	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
160	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
161	instantiation	175	⊢
	: , :
162	instantiation	175	⊢
	: , :
163	instantiation	176, 178	⊢
	:
164	instantiation	177, 178	⊢
	:
165	instantiation	192, 190, 179	⊢
	: , : , :
166	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
167	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
168	instantiation	180, 183	⊢
	:
169	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
170	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
171	instantiation	181, 182	⊢
	:
172	instantiation	192, 190, 183	⊢
	: , : , :
173	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
174	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
175	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
176	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
177	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
178	instantiation	192, 184, 185	⊢
	: , : , :
179	instantiation	192, 193, 186	⊢
	: , : , :
180	theorem		⊢
	proveit.numbers.negation.int_closure
181	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
182	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int
183	instantiation	192, 193, 187	⊢
	: , : , :
184	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
185	instantiation	192, 188, 189	⊢
	: , : , :
186	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
187	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
188	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
189	instantiation	192, 190, 191	⊢
	: , : , :
190	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
191	instantiation	192, 193, 194	⊢
	: , : , :
192	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
193	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
194	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements