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	67	⊢
2	instantiation	15, 4	⊢
	: , : , :
3	instantiation	67, 5, 6	⊢
	: , : , :
4	instantiation	67, 7, 8	⊢
	: , : , :
5	instantiation	67, 9, 10	⊢
	: , : , :
6	instantiation	11, 20	⊢
	:
7	instantiation	15, 12	⊢
	: , : , :
8	instantiation	13, 37, 14*	⊢
	:
9	instantiation	15, 16	⊢
	: , : , :
10	instantiation	17, 18, 19, 20, 21*	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.division.frac_one_denom
12	instantiation	22, 23	⊢
	:
13	theorem		⊢
	proveit.numbers.absolute_value.abs_even
14	instantiation	24, 25, 26, 87, 88, 109, 89, 27*	⊢
	: , :
15	axiom		⊢
	proveit.logic.equality.substitution
16	instantiation	67, 28, 29	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.division.frac_cancel_left
18	instantiation	123, 31, 30	⊢
	: , : , :
19	instantiation	123, 31, 32	⊢
	: , : , :
20	instantiation	49, 33, 34	⊢
	: , : , :
21	instantiation	35, 87	⊢
	:
22	theorem		⊢
	proveit.numbers.addition.elim_zero_left
23	instantiation	36, 37	⊢
	:
24	theorem		⊢
	proveit.numbers.absolute_value.abs_prod
25	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
26	instantiation	38	⊢
	: , : , : , :
27	instantiation	67, 39, 40	⊢
	: , : , :
28	instantiation	58, 83, 80, 125, 84, 41, 89, 87, 88, 61	⊢
	: , : , : , : , : , : , :
29	instantiation	42, 80, 59, 83, 43, 84, 87, 89, 88, 61	⊢
	: , : , : , : , : , :
30	instantiation	123, 45, 44	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
32	instantiation	123, 45, 46	⊢
	: , : , :
33	instantiation	123, 117, 47	⊢
	: , : , :
34	instantiation	82, 83, 125, 80, 84, 48, 89, 88, 61	⊢
	: , : , : , : , : , :
35	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
36	theorem		⊢
	proveit.numbers.negation.complex_closure
37	instantiation	49, 50, 51	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
39	instantiation	52, 59, 53, 54, 55, 56, 57	⊢
	: , : , : , :
40	instantiation	58, 83, 59, 84, 60, 87, 88, 61, 89	⊢
	: , : , : , : , : , : , :
41	instantiation	96	⊢
	: , :
42	theorem		⊢
	proveit.numbers.multiplication.association
43	instantiation	74	⊢
	: , : , :
44	instantiation	123, 63, 62	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
46	instantiation	123, 63, 64	⊢
	: , : , :
47	instantiation	102, 65, 75	⊢
	: , :
48	instantiation	96	⊢
	: , :
49	theorem		⊢
	proveit.logic.equality.sub_right_side_into
50	instantiation	123, 117, 66	⊢
	: , : , :
51	instantiation	67, 68, 69	⊢
	: , : , :
52	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
53	instantiation	74	⊢
	: , : , :
54	instantiation	74	⊢
	: , : , :
55	instantiation	72, 70	⊢
	:
56	instantiation	72, 71	⊢
	:
57	instantiation	72, 73	⊢
	:
58	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
59	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
60	instantiation	74	⊢
	: , : , :
61	instantiation	123, 117, 75	⊢
	: , : , :
62	instantiation	123, 77, 76	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
64	instantiation	123, 77, 78	⊢
	: , : , :
65	instantiation	102, 97, 104	⊢
	: , :
66	instantiation	102, 95, 79	⊢
	: , :
67	axiom		⊢
	proveit.logic.equality.equals_transitivity
68	instantiation	82, 80, 125, 83, 86, 84, 81, 109, 89	⊢
	: , : , : , : , : , :
69	instantiation	82, 83, 125, 84, 85, 86, 87, 88, 109, 89	⊢
	: , : , : , : , : , :
70	instantiation	90, 125	⊢
	:
71	instantiation	92, 91	⊢
	: , :
72	theorem		⊢
	proveit.numbers.absolute_value.abs_non_neg_elim
73	instantiation	92, 93	⊢
	: , :
74	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
75	instantiation	123, 113, 94	⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
77	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
78	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
79	instantiation	102, 118, 97	⊢
	: , :
80	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
81	instantiation	123, 117, 95	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.multiplication.disassociation
83	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
84	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
85	instantiation	96	⊢
	: , :
86	instantiation	96	⊢
	: , :
87	instantiation	123, 117, 103	⊢
	: , : , :
88	instantiation	123, 117, 104	⊢
	: , : , :
89	instantiation	123, 117, 97	⊢
	: , : , :
90	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
91	instantiation	98, 114	⊢
	:
92	theorem		⊢
	proveit.numbers.ordering.relax_less
93	instantiation	99, 107	⊢
	:
94	instantiation	100, 101	⊢
	:
95	instantiation	102, 103, 104	⊢
	: , :
96	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
97	instantiation	105, 106, 107	⊢
	: , : , :
98	theorem		⊢
	proveit.numbers.number_sets.real_numbers.positive_if_in_real_pos
99	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
100	theorem		⊢
	proveit.numbers.absolute_value.abs_nonzero_closure
101	instantiation	108, 109, 110	⊢
	:
102	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
103	instantiation	123, 111, 112	⊢
	: , : , :
104	instantiation	123, 113, 114	⊢
	: , : , :
105	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
106	instantiation	115, 116	⊢
	: , :
107	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
108	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
109	instantiation	123, 117, 118	⊢
	: , : , :
110	assumption		⊢
111	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
112	instantiation	123, 119, 120	⊢
	: , : , :
113	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
114	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
115	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
116	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
117	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
118	instantiation	121, 122	⊢
	:
119	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
120	instantiation	123, 124, 125	⊢
	: , : , :
121	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
122	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int
123	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
124	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
125	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements