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