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	generalization	1	⊢
1	instantiation	2, 12, 3, 4	⊢
	: , :
2	theorem		⊢
	proveit.numbers.modular.mod_abs_x_reduce_to_abs_x
3	instantiation	208, 5, 6	⊢
	: , : , :
4	instantiation	7, 8, 9	⊢
	: , : , :
5	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
6	instantiation	208, 10, 168	⊢
	: , : , :
7	theorem		⊢
	proveit.logic.equality.sub_right_side_into
8	instantiation	11, 12, 13, 86, 14, 15*	⊢
	: , : , :
9	instantiation	131, 121, 16, 17	⊢
	: , : , : , :
10	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
11	theorem		⊢
	proveit.numbers.absolute_value.weak_upper_bound_asym_interval
12	instantiation	208, 197, 18	⊢
	: , : , :
13	instantiation	208, 197, 19	⊢
	: , : , :
14	instantiation	20, 21, 22	⊢
	: , :
15	instantiation	115, 23, 24	⊢
	: , : , :
16	instantiation	146, 25	⊢
	: , : , :
17	instantiation	144, 26	⊢
	: , :
18	instantiation	208, 204, 27	⊢
	: , : , :
19	instantiation	208, 204, 51	⊢
	: , : , :
20	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
21	instantiation	28, 51, 111, 39	⊢
	: , : , :
22	instantiation	29, 51, 111, 39	⊢
	: , : , :
23	instantiation	70, 210, 30, 31, 32, 33	⊢
	: , : , : , :
24	instantiation	115, 34, 35	⊢
	: , : , :
25	instantiation	146, 167	⊢
	: , : , :
26	instantiation	36, 138, 179, 166, 37*	⊢
	: , :
27	instantiation	208, 38, 39	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
29	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
30	instantiation	135	⊢
	: , :
31	instantiation	135	⊢
	: , :
32	instantiation	40, 41, 42*	⊢
	:
33	instantiation	43, 44	⊢
	:
34	instantiation	45, 94, 86	⊢
	: , :
35	instantiation	46, 86, 94, 47*	⊢
	: , :
36	theorem		⊢
	proveit.numbers.division.div_as_mult
37	instantiation	115, 48, 49	⊢
	: , : , :
38	instantiation	50, 51, 111	⊢
	: , :
39	assumption		⊢
40	theorem		⊢
	proveit.numbers.absolute_value.abs_neg_elim
41	instantiation	52, 76, 176, 86, 53, 54*, 55*	⊢
	: , : , :
42	instantiation	56, 64, 164, 57*	⊢
	: , :
43	theorem		⊢
	proveit.numbers.absolute_value.abs_non_neg_elim
44	instantiation	90, 58	⊢
	: , :
45	theorem		⊢
	proveit.numbers.ordering.max_bin_args_commute
46	axiom		⊢
	proveit.numbers.ordering.max_def_bin
47	instantiation	115, 59, 60	⊢
	: , : , :
48	instantiation	146, 61	⊢
	: , : , :
49	instantiation	62, 138, 63	⊢
	: , :
50	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
51	instantiation	152, 88, 196	⊢
	: , :
52	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
53	instantiation	171, 118	⊢
	:
54	instantiation	157, 164, 64	⊢
	: , :
55	instantiation	115, 65, 66	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
57	instantiation	67, 68	⊢
	:
58	instantiation	69, 118	⊢
	:
59	instantiation	70, 210, 71, 72, 73, 74	⊢
	: , : , : , :
60	instantiation	75, 123, 203, 125	⊢
	: , : , : , : , :
61	instantiation	161, 162, 207, 167*	⊢
	: , :
62	theorem		⊢
	proveit.numbers.multiplication.commutation
63	instantiation	148, 164, 179, 166	⊢
	: , :
64	instantiation	208, 188, 76	⊢
	: , : , :
65	instantiation	115, 77, 78	⊢
	: , : , :
66	instantiation	79, 127, 104	⊢
	: , :
67	theorem		⊢
	proveit.numbers.negation.double_negation
68	instantiation	208, 188, 86	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
70	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
71	instantiation	135	⊢
	: , :
72	instantiation	135	⊢
	: , :
73	instantiation	80, 87	⊢
	: , :
74	instantiation	81, 82	⊢
	: , :
75	axiom		⊢
	proveit.core_expr_types.conditionals.true_case_reduction
76	instantiation	208, 197, 83	⊢
	: , : , :
77	instantiation	146, 121	⊢
	: , : , :
78	instantiation	146, 84	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
80	theorem		⊢
	proveit.core_expr_types.conditionals.satisfied_condition_reduction
81	theorem		⊢
	proveit.core_expr_types.conditionals.dissatisfied_condition_reduction
82	instantiation	85, 94, 86, 87	⊢
	: , :
83	instantiation	208, 204, 88	⊢
	: , : , :
84	instantiation	146, 121	⊢
	: , : , :
85	theorem		⊢
	proveit.numbers.ordering.not_less_from_less_eq
86	instantiation	208, 197, 89	⊢
	: , : , :
87	instantiation	90, 91	⊢
	: , :
88	instantiation	92, 111	⊢
	:
89	instantiation	208, 204, 111	⊢
	: , : , :
90	theorem		⊢
	proveit.numbers.ordering.relax_less
91	instantiation	93, 94, 95, 176, 96, 97*, 98*	⊢
	: , : , :
92	theorem		⊢
	proveit.numbers.negation.int_closure
93	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
94	instantiation	208, 197, 99	⊢
	: , : , :
95	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
96	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
97	instantiation	131, 100, 101, 102	⊢
	: , : , : , :
98	instantiation	131, 103, 104, 105	⊢
	: , : , : , :
99	instantiation	208, 204, 106	⊢
	: , : , :
100	instantiation	115, 107, 108	⊢
	: , : , :
101	instantiation	139	⊢
	:
102	instantiation	144, 114	⊢
	: , :
103	instantiation	115, 109, 110	⊢
	: , : , :
104	instantiation	139	⊢
	:
105	instantiation	144, 121	⊢
	: , :
106	instantiation	152, 111, 154	⊢
	: , :
107	instantiation	146, 114	⊢
	: , : , :
108	instantiation	115, 112, 113	⊢
	: , : , :
109	instantiation	146, 114	⊢
	: , : , :
110	instantiation	115, 116, 117	⊢
	: , : , :
111	instantiation	208, 169, 118	⊢
	: , : , :
112	instantiation	122, 203, 210, 123, 124, 125, 119, 127, 159	⊢
	: , : , : , : , : , :
113	instantiation	120, 123, 210, 125, 124, 127, 159	⊢
	: , : , : , :
114	instantiation	146, 121	⊢
	: , : , :
115	axiom		⊢
	proveit.logic.equality.equals_transitivity
116	instantiation	122, 203, 210, 123, 124, 125, 164, 127, 159	⊢
	: , : , : , : , : , :
117	instantiation	126, 164, 127, 128	⊢
	: , : , :
118	instantiation	129, 210, 130	⊢
	: , :
119	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
120	theorem		⊢
	proveit.numbers.addition.elim_zero_any
121	instantiation	131, 132, 133, 134	⊢
	: , : , : , :
122	theorem		⊢
	proveit.numbers.addition.disassociation
123	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
124	instantiation	135	⊢
	: , :
125	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
126	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
127	instantiation	136, 137, 138	⊢
	: , :
128	instantiation	139	⊢
	:
129	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
130	instantiation	140, 141, 142	⊢
	:
131	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
132	instantiation	146, 143	⊢
	: , : , :
133	instantiation	144, 145	⊢
	: , :
134	instantiation	146, 147	⊢
	: , : , :
135	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
136	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
137	instantiation	148, 164, 149, 150	⊢
	: , :
138	instantiation	208, 188, 151	⊢
	: , : , :
139	axiom		⊢
	proveit.logic.equality.equals_reflexivity
140	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
141	instantiation	152, 153, 154	⊢
	: , :
142	instantiation	155, 156	⊢
	: , :
143	instantiation	157, 158, 159	⊢
	: , :
144	theorem		⊢
	proveit.logic.equality.equals_reversal
145	instantiation	160, 179, 173, 172, 166	⊢
	: , : , :
146	axiom		⊢
	proveit.logic.equality.substitution
147	instantiation	161, 162, 207	⊢
	: , :
148	theorem		⊢
	proveit.numbers.division.div_complex_closure
149	instantiation	163, 179, 164	⊢
	: , :
150	instantiation	165, 166, 167	⊢
	: , : , :
151	instantiation	180, 181, 168	⊢
	: , : , :
152	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
153	instantiation	208, 169, 182	⊢
	: , : , :
154	instantiation	208, 170, 200	⊢
	: , : , :
155	theorem		⊢
	proveit.numbers.addition.subtraction.nonneg_difference
156	instantiation	171, 182	⊢
	:
157	theorem		⊢
	proveit.numbers.addition.commutation
158	instantiation	208, 188, 172	⊢
	: , : , :
159	instantiation	208, 188, 173	⊢
	: , : , :
160	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
161	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
162	instantiation	208, 174, 175	⊢
	: , : , :
163	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
164	instantiation	208, 188, 176	⊢
	: , : , :
165	theorem		⊢
	proveit.logic.equality.sub_left_side_into
166	instantiation	177, 202	⊢
	:
167	instantiation	178, 179	⊢
	:
168	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
169	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
170	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
171	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
172	instantiation	180, 181, 182	⊢
	: , : , :
173	instantiation	208, 183, 184	⊢
	: , : , :
174	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
175	instantiation	208, 185, 186	⊢
	: , : , :
176	instantiation	208, 197, 187	⊢
	: , : , :
177	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
178	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
179	instantiation	208, 188, 189	⊢
	: , : , :
180	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
181	instantiation	190, 191	⊢
	: , :
182	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
183	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
184	instantiation	208, 192, 193	⊢
	: , : , :
185	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
186	instantiation	208, 194, 195	⊢
	: , : , :
187	instantiation	208, 204, 196	⊢
	: , : , :
188	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
189	instantiation	208, 197, 198	⊢
	: , : , :
190	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
191	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
192	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_neg_within_real_neg
193	instantiation	208, 199, 200	⊢
	: , : , :
194	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
195	instantiation	208, 201, 202	⊢
	: , : , :
196	instantiation	208, 209, 203	⊢
	: , : , :
197	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
198	instantiation	208, 204, 205	⊢
	: , : , :
199	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.neg_int_within_rational_neg
200	instantiation	206, 207	⊢
	:
201	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
202	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
203	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
204	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
205	instantiation	208, 209, 210	⊢
	: , : , :
206	theorem		⊢
	proveit.numbers.negation.int_neg_closure
207	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
208	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
209	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
210	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements