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	69	⊢
2	instantiation	4, 9, 10, 107, 11, 5, 89, 24, 15, 14, 16	⊢
	: , : , : , : , : , : , :
3	instantiation	69, 6, 7	⊢
	: , : , :
4	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
5	instantiation	19	⊢
	: , : , :
6	instantiation	8, 9, 114, 10, 11, 12, 13, 14, 89, 24, 15, 16	⊢
	: , : , : , : , : , :
7	instantiation	78, 17	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.multiplication.association
9	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
10	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
11	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
12	instantiation	18	⊢
	: , :
13	instantiation	19	⊢
	: , : , :
14	instantiation	20, 63, 89, 21	⊢
	: , :
15	instantiation	112, 95, 22	⊢
	: , : , :
16	instantiation	23, 24, 25	⊢
	: , :
17	instantiation	34, 26, 27	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
19	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
20	theorem		⊢
	proveit.numbers.division.div_complex_closure
21	instantiation	28, 101	⊢
	:
22	instantiation	29, 30, 31	⊢
	: , :
23	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
24	instantiation	112, 95, 32	⊢
	: , : , :
25	instantiation	112, 95, 33	⊢
	: , : , :
26	instantiation	34, 35, 36	⊢
	: , : , :
27	instantiation	37, 38, 39, 40	⊢
	: , : , : , :
28	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
29	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
30	instantiation	41, 42	⊢
	:
31	instantiation	43, 44	⊢
	:
32	instantiation	112, 45, 46	⊢
	: , : , :
33	instantiation	112, 103, 47	⊢
	: , : , :
34	theorem		⊢
	proveit.logic.equality.sub_right_side_into
35	instantiation	48, 63, 49, 50	⊢
	: , : , : , : , :
36	instantiation	69, 51, 52	⊢
	: , : , :
37	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
38	instantiation	78, 53	⊢
	: , : , :
39	instantiation	78, 53	⊢
	: , : , :
40	instantiation	88, 63	⊢
	:
41	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
42	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
43	theorem		⊢
	proveit.numbers.negation.real_closure
44	instantiation	54, 55, 56	⊢
	: , :
45	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
46	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
47	instantiation	112, 108, 57	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_denom_left
49	instantiation	112, 59, 58	⊢
	: , : , :
50	instantiation	112, 59, 60	⊢
	: , : , :
51	instantiation	78, 61	⊢
	: , : , :
52	instantiation	78, 62	⊢
	: , : , :
53	instantiation	80, 63	⊢
	:
54	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
55	instantiation	112, 103, 64	⊢
	: , : , :
56	instantiation	112, 103, 65	⊢
	: , : , :
57	instantiation	105, 99	⊢
	:
58	instantiation	112, 67, 66	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
60	instantiation	112, 67, 85	⊢
	: , : , :
61	instantiation	78, 68	⊢
	: , : , :
62	instantiation	69, 70, 71	⊢
	: , : , :
63	instantiation	112, 95, 72	⊢
	: , : , :
64	instantiation	112, 108, 73	⊢
	: , : , :
65	instantiation	112, 74, 75	⊢
	: , : , :
66	instantiation	112, 92, 76	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
68	instantiation	77, 89	⊢
	:
69	axiom		⊢
	proveit.logic.equality.equals_transitivity
70	instantiation	78, 79	⊢
	: , : , :
71	instantiation	80, 89	⊢
	:
72	instantiation	112, 103, 81	⊢
	: , : , :
73	instantiation	112, 82, 83	⊢
	: , : , :
74	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational
75	instantiation	84, 85, 86	⊢
	: , :
76	instantiation	112, 100, 87	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
78	axiom		⊢
	proveit.logic.equality.substitution
79	instantiation	88, 89	⊢
	:
80	theorem		⊢
	proveit.numbers.division.frac_one_denom
81	instantiation	112, 108, 99	⊢
	: , : , :
82	instantiation	90, 91, 106	⊢
	: , :
83	assumption		⊢
84	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_nonzero_closure
85	instantiation	112, 92, 93	⊢
	: , : , :
86	instantiation	105, 94	⊢
	:
87	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
88	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
89	instantiation	112, 95, 96	⊢
	: , : , :
90	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
91	instantiation	97, 98, 99	⊢
	: , :
92	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
93	instantiation	112, 100, 101	⊢
	: , : , :
94	instantiation	112, 110, 102	⊢
	: , : , :
95	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
96	instantiation	112, 103, 104	⊢
	: , : , :
97	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
98	instantiation	105, 106	⊢
	:
99	instantiation	112, 113, 107	⊢
	: , : , :
100	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
101	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
102	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
103	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
104	instantiation	112, 108, 109	⊢
	: , : , :
105	theorem		⊢
	proveit.numbers.negation.int_closure
106	instantiation	112, 110, 111	⊢
	: , : , :
107	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
108	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
109	instantiation	112, 113, 114	⊢
	: , : , :
110	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
111	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
112	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
113	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
114	theorem		⊢
	proveit.numbers.numerals.decimals.nat2