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_left_side_into
2	instantiation	4, 5, 6, 21, 19	⊢
	: , :
3	instantiation	100, 7, 8, 9	⊢
	: , : , : , :
4	theorem		⊢
	proveit.logic.booleans.disjunction.right_if_not_left
5	instantiation	10, 11	⊢
	:
6	instantiation	12, 13	⊢
	: , :
7	instantiation	14, 15, 16, 17, 18*	⊢
	: , :
8	instantiation	141, 72	⊢
	:
9	instantiation	126	⊢
	:
10	axiom		⊢
	proveit.logic.booleans.negation.operand_is_bool
11	instantiation	20, 19	⊢
	:
12	axiom		⊢
	proveit.logic.booleans.disjunction.right_in_bool
13	instantiation	20, 21	⊢
	:
14	theorem		⊢
	proveit.numbers.division.div_as_mult
15	instantiation	97, 22, 23	⊢
	: , : , :
16	instantiation	159, 152, 38	⊢
	: , : , :
17	instantiation	24, 161, 33, 112, 25	⊢
	: , :
18	instantiation	134, 26, 27	⊢
	: , : , :
19	instantiation	28, 29	⊢
	: , :
20	theorem		⊢
	proveit.logic.booleans.in_bool_if_true
21	instantiation	30, 31	⊢
	:
22	instantiation	159, 152, 32	⊢
	: , : , :
23	instantiation	56, 66, 161, 154, 68, 33, 150, 107, 72	⊢
	: , : , : , : , : , :
24	theorem		⊢
	proveit.numbers.multiplication.mult_not_eq_zero
25	instantiation	159, 121, 88	⊢
	: , : , :
26	instantiation	142, 34	⊢
	: , : , :
27	instantiation	134, 35, 36	⊢
	: , : , :
28	theorem		⊢
	proveit.logic.equality.unfold_not_equals
29	assumption		⊢
30	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_zero_or_non_int
31	instantiation	37, 154, 66, 68	⊢
	: , : , : , : , :
32	instantiation	45, 38, 82	⊢
	: , :
33	instantiation	79	⊢
	: , :
34	instantiation	39, 150, 107, 96, 93, 76, 40*	⊢
	: , : , :
35	instantiation	134, 41, 42	⊢
	: , : , :
36	instantiation	134, 43, 44	⊢
	: , : , :
37	theorem		⊢
	proveit.logic.sets.enumeration.in_enumerated_set
38	instantiation	45, 153, 118	⊢
	: , :
39	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_product
40	instantiation	46, 112, 146, 47*	⊢
	: , :
41	instantiation	134, 48, 49	⊢
	: , : , :
42	instantiation	134, 50, 51	⊢
	: , : , :
43	instantiation	52, 66, 67, 68, 70, 107, 72, 73	⊢
	: , : , : , :
44	instantiation	134, 53, 54	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
46	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
47	instantiation	89, 150	⊢
	:
48	instantiation	56, 66, 67, 154, 68, 58, 150, 107, 72, 55	⊢
	: , : , : , : , : , :
49	instantiation	56, 67, 161, 66, 58, 57, 68, 150, 107, 72, 71, 73	⊢
	: , : , : , : , : , :
50	instantiation	61, 66, 67, 154, 68, 58, 150, 107, 72, 71, 73	⊢
	: , : , : , : , : , : , :
51	instantiation	134, 59, 60	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
53	instantiation	61, 154, 66, 68, 107, 72, 73	⊢
	: , : , : , : , : , : , :
54	instantiation	65, 66, 161, 154, 68, 62, 107, 73, 72, 63*	⊢
	: , : , : , : , : , :
55	instantiation	64, 71, 73	⊢
	: , :
56	theorem		⊢
	proveit.numbers.multiplication.disassociation
57	instantiation	79	⊢
	: , :
58	instantiation	80	⊢
	: , : , :
59	instantiation	65, 66, 161, 67, 68, 69, 70, 71, 150, 107, 72, 73	⊢
	: , : , : , : , : , :
60	instantiation	142, 74	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
62	instantiation	79	⊢
	: , :
63	instantiation	75, 107, 137, 96, 76, 77*, 78*	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
65	theorem		⊢
	proveit.numbers.multiplication.association
66	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
67	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
68	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
69	instantiation	79	⊢
	: , :
70	instantiation	80	⊢
	: , : , :
71	instantiation	159, 152, 81	⊢
	: , : , :
72	instantiation	159, 152, 82	⊢
	: , : , :
73	instantiation	83, 107, 84	⊢
	: , :
74	instantiation	97, 85, 86	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
76	instantiation	87, 88	⊢
	:
77	instantiation	89, 107	⊢
	:
78	instantiation	134, 90, 91	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
80	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
81	instantiation	92, 137, 153, 93	⊢
	: , :
82	instantiation	94, 95	⊢
	:
83	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
84	instantiation	159, 152, 96	⊢
	: , : , :
85	instantiation	97, 98, 99	⊢
	: , : , :
86	instantiation	100, 101, 102, 103	⊢
	: , : , : , :
87	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
88	instantiation	159, 104, 128	⊢
	: , : , :
89	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
90	instantiation	142, 105	⊢
	: , : , :
91	instantiation	106, 107	⊢
	:
92	theorem		⊢
	proveit.numbers.division.div_real_closure
93	instantiation	108, 148	⊢
	:
94	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
95	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int
96	instantiation	159, 155, 109	⊢
	: , : , :
97	theorem		⊢
	proveit.logic.equality.sub_right_side_into
98	instantiation	110, 125, 111, 112	⊢
	: , : , : , : , :
99	instantiation	134, 113, 114	⊢
	: , : , :
100	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
101	instantiation	142, 115	⊢
	: , : , :
102	instantiation	142, 115	⊢
	: , : , :
103	instantiation	149, 125	⊢
	:
104	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
105	instantiation	116, 125, 117	⊢
	: , :
106	theorem		⊢
	proveit.numbers.exponentiation.exp_zero_eq_one
107	instantiation	159, 152, 118	⊢
	: , : , :
108	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
109	instantiation	159, 157, 119	⊢
	: , : , :
110	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_denom_left
111	instantiation	159, 121, 120	⊢
	: , : , :
112	instantiation	159, 121, 122	⊢
	: , : , :
113	instantiation	142, 123	⊢
	: , : , :
114	instantiation	142, 124	⊢
	: , : , :
115	instantiation	144, 125	⊢
	:
116	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
117	instantiation	126	⊢
	:
118	instantiation	159, 127, 128	⊢
	: , : , :
119	instantiation	129, 151	⊢
	:
120	instantiation	159, 131, 130	⊢
	: , : , :
121	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
122	instantiation	159, 131, 132	⊢
	: , : , :
123	instantiation	142, 133	⊢
	: , : , :
124	instantiation	134, 135, 136	⊢
	: , : , :
125	instantiation	159, 152, 137	⊢
	: , : , :
126	axiom		⊢
	proveit.logic.equality.equals_reflexivity
127	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
128	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
129	theorem		⊢
	proveit.numbers.negation.int_closure
130	instantiation	159, 139, 138	⊢
	: , : , :
131	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
132	instantiation	159, 139, 140	⊢
	: , : , :
133	instantiation	141, 150	⊢
	:
134	axiom		⊢
	proveit.logic.equality.equals_transitivity
135	instantiation	142, 143	⊢
	: , : , :
136	instantiation	144, 150	⊢
	:
137	instantiation	159, 155, 145	⊢
	: , : , :
138	instantiation	159, 147, 146	⊢
	: , : , :
139	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
140	instantiation	159, 147, 148	⊢
	: , : , :
141	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
142	axiom		⊢
	proveit.logic.equality.substitution
143	instantiation	149, 150	⊢
	:
144	theorem		⊢
	proveit.numbers.division.frac_one_denom
145	instantiation	159, 157, 151	⊢
	: , : , :
146	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
147	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
148	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
149	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
150	instantiation	159, 152, 153	⊢
	: , : , :
151	instantiation	159, 160, 154	⊢
	: , : , :
152	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
153	instantiation	159, 155, 156	⊢
	: , : , :
154	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
155	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
156	instantiation	159, 157, 158	⊢
	: , : , :
157	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
158	instantiation	159, 160, 161	⊢
	: , : , :
159	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
160	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
161	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements