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.numbers.ordering.transitivity_less_eq_less_eq
2	instantiation	55, 4, 5, 6*	⊢
	: , : , :
3	instantiation	64, 7, 8	⊢
	: , : , :
4	instantiation	9, 10, 11, 15, 12*	⊢
	: , : , :
5	instantiation	19, 45, 68	⊢
	: , :
6	instantiation	13, 14, 15, 16, 17*	⊢
	: , :
7	instantiation	24, 18	⊢
	: , :
8	instantiation	19, 20, 67	⊢
	: , :
9	theorem		⊢
	proveit.numbers.modular.mod_abs_of_difference_bound
10	instantiation	97, 76, 54	⊢
	: , :
11	instantiation	97, 76, 29	⊢
	: , :
12	instantiation	110, 21, 22	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.modular.mod_abs_x_reduce_to_abs_x
14	instantiation	97, 79, 54	⊢
	: , :
15	instantiation	23, 81, 144	⊢
	: , :
16	instantiation	24, 25	⊢
	: , :
17	instantiation	26, 27, 28*	⊢
	:
18	instantiation	47, 149, 150, 93	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.addition.commutation
20	instantiation	170, 143, 29	⊢
	: , : , :
21	instantiation	69, 30	⊢
	: , : , :
22	instantiation	31, 32, 33, 34	⊢
	: , : , : , :
23	theorem		⊢
	proveit.numbers.exponentiation.exp_real_pos_closure
24	theorem		⊢
	proveit.numbers.ordering.relax_less
25	instantiation	35, 36, 37	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.absolute_value.abs_neg_elim
27	instantiation	38, 39	⊢
	: , :
28	instantiation	40, 68, 67	⊢
	: , :
29	instantiation	63, 79	⊢
	:
30	instantiation	40, 62, 68	⊢
	: , :
31	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
32	instantiation	122, 123, 167, 172, 125, 42, 62, 45, 41	⊢
	: , : , : , : , : , :
33	instantiation	122, 167, 123, 42, 43, 125, 62, 45, 53, 68	⊢
	: , : , : , : , : , :
34	instantiation	44, 123, 172, 125, 62, 45, 68, 46	⊢
	: , : , : , : , : , : , : , :
35	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
36	instantiation	47, 149, 150, 48	⊢
	: , : , :
37	instantiation	64, 49, 50	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.addition.subtraction.nonpos_difference
39	instantiation	51, 121	⊢
	:
40	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_subtract
41	instantiation	52, 53, 68	⊢
	: , :
42	instantiation	141	⊢
	: , :
43	instantiation	141	⊢
	: , :
44	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general
45	instantiation	170, 143, 54	⊢
	: , : , :
46	instantiation	145	⊢
	:
47	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
48	instantiation	55, 56, 57	⊢
	: , : , :
49	instantiation	58, 117	⊢
	:
50	instantiation	110, 59, 60	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.rounding.floor_x_le_x
52	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
53	instantiation	61, 62	⊢
	:
54	instantiation	63, 121	⊢
	:
55	theorem		⊢
	proveit.logic.equality.sub_right_side_into
56	instantiation	64, 93, 65	⊢
	: , : , :
57	instantiation	66, 67, 68	⊢
	: , :
58	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
59	instantiation	69, 70	⊢
	: , : , :
60	instantiation	71, 72, 73, 90, 74*, 75*	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.negation.complex_closure
62	instantiation	170, 143, 76	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.negation.real_closure
64	theorem		⊢
	proveit.logic.equality.sub_left_side_into
65	instantiation	77, 78	⊢
	:
66	theorem		⊢
	proveit.numbers.absolute_value.abs_diff_reversal
67	instantiation	170, 143, 121	⊢
	: , : , :
68	instantiation	170, 143, 79	⊢
	: , : , :
69	axiom		⊢
	proveit.logic.equality.substitution
70	instantiation	80, 81, 144, 150, 82, 83, 84*	⊢
	: , : , : , :
71	theorem		⊢
	proveit.numbers.division.frac_cancel_left
72	instantiation	170, 86, 85	⊢
	: , : , :
73	instantiation	170, 86, 87	⊢
	: , : , :
74	instantiation	88, 101	⊢
	:
75	instantiation	89, 90	⊢
	:
76	instantiation	170, 156, 91	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.absolute_value.abs_non_neg_elim
78	instantiation	92, 149, 150, 93	⊢
	: , : , :
79	instantiation	170, 156, 94	⊢
	: , : , :
80	theorem		⊢
	proveit.numbers.exponentiation.exp_factored_real
81	instantiation	170, 95, 96	⊢
	: , : , :
82	instantiation	97, 144, 142	⊢
	: , :
83	instantiation	98, 99	⊢
	: , :
84	instantiation	100, 101	⊢
	:
85	instantiation	170, 103, 102	⊢
	: , : , :
86	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
87	instantiation	170, 103, 104	⊢
	: , : , :
88	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
89	theorem		⊢
	proveit.numbers.division.frac_one_denom
90	instantiation	170, 143, 105	⊢
	: , : , :
91	instantiation	170, 164, 106	⊢
	: , : , :
92	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
93	instantiation	107, 121	⊢
	:
94	instantiation	170, 164, 108	⊢
	: , : , :
95	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
96	instantiation	170, 109, 132	⊢
	: , : , :
97	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
98	theorem		⊢
	proveit.logic.equality.equals_reversal
99	instantiation	110, 111, 112	⊢
	: , : , :
100	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
101	instantiation	170, 143, 113	⊢
	: , : , :
102	instantiation	170, 115, 114	⊢
	: , : , :
103	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
104	instantiation	170, 115, 116	⊢
	: , : , :
105	instantiation	153, 154, 117	⊢
	: , : , :
106	instantiation	170, 118, 119	⊢
	: , : , :
107	theorem		⊢
	proveit.numbers.rounding.real_minus_floor_interval
108	instantiation	120, 121	⊢
	:
109	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
110	axiom		⊢
	proveit.logic.equality.equals_transitivity
111	instantiation	122, 172, 167, 123, 124, 125, 128, 129, 126	⊢
	: , : , : , : , : , :
112	instantiation	127, 128, 129, 130	⊢
	: , : , :
113	instantiation	170, 156, 131	⊢
	: , : , :
114	instantiation	170, 133, 132	⊢
	: , : , :
115	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
116	instantiation	170, 133, 134	⊢
	: , : , :
117	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
118	instantiation	135, 136, 137	⊢
	: , :
119	assumption		⊢
120	axiom		⊢
	proveit.numbers.rounding.floor_is_an_int
121	instantiation	138, 139, 140	⊢
	: , :
122	theorem		⊢
	proveit.numbers.addition.disassociation
123	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
124	instantiation	141	⊢
	: , :
125	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
126	instantiation	170, 143, 142	⊢
	: , : , :
127	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
128	instantiation	170, 143, 150	⊢
	: , : , :
129	instantiation	170, 143, 144	⊢
	: , : , :
130	instantiation	145	⊢
	:
131	instantiation	170, 164, 162	⊢
	: , : , :
132	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
133	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
134	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
135	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
136	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
137	instantiation	146, 155, 158	⊢
	: , :
138	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
139	instantiation	170, 156, 147	⊢
	: , : , :
140	instantiation	148, 149, 150, 151	⊢
	: , : , :
141	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
142	instantiation	170, 156, 152	⊢
	: , : , :
143	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
144	instantiation	153, 154, 169	⊢
	: , : , :
145	axiom		⊢
	proveit.logic.equality.equals_reflexivity
146	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
147	instantiation	170, 164, 155	⊢
	: , : , :
148	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
149	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
150	instantiation	170, 156, 157	⊢
	: , : , :
151	axiom		⊢
	proveit.physics.quantum.QPE._phase_in_interval
152	instantiation	170, 164, 158	⊢
	: , : , :
153	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
154	instantiation	159, 160	⊢
	: , :
155	instantiation	161, 162, 163	⊢
	: , :
156	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
157	instantiation	170, 164, 166	⊢
	: , : , :
158	instantiation	165, 166	⊢
	:
159	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
160	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
161	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
162	instantiation	170, 171, 167	⊢
	: , : , :
163	instantiation	170, 168, 169	⊢
	: , : , :
164	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
165	theorem		⊢
	proveit.numbers.negation.int_closure
166	instantiation	170, 171, 172	⊢
	: , : , :
167	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
168	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
169	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
170	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
171	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
172	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements