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