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