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