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