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