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	theorem		⊢
	proveit.logic.equality.sub_left_side_into
2	instantiation	4, 5	⊢
	:
3	instantiation	59, 6, 7	⊢
	: , : , :
4	theorem		⊢
	proveit.numbers.rounding.real_minus_floor_interval
5	instantiation	8, 82, 45	⊢
	: , :
6	instantiation	29, 9, 10	⊢
	: , : , :
7	instantiation	69, 11	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
9	instantiation	29, 12, 13	⊢
	: , : , :
10	instantiation	29, 14, 28	⊢
	: , : , :
11	instantiation	69, 15	⊢
	: , : , :
12	instantiation	69, 16	⊢
	: , : , :
13	instantiation	17, 107, 18, 19, 79, 37, 20, 21*	⊢
	: , : , : , : , : , :
14	axiom		⊢
	proveit.physics.quantum.QPE._best_floor_def
15	instantiation	22, 23	⊢
	: , :
16	instantiation	24, 80	⊢
	:
17	theorem		⊢
	proveit.numbers.multiplication.distribute_through_subtract
18	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
19	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
20	instantiation	25, 53, 79, 47	⊢
	: , :
21	instantiation	29, 26, 27	⊢
	: , : , :
22	theorem		⊢
	proveit.logic.equality.equals_reversal
23	instantiation	69, 28	⊢
	: , : , :
24	axiom		⊢
	proveit.physics.quantum.QPE._delta_b_def
25	theorem		⊢
	proveit.numbers.division.div_complex_closure
26	instantiation	29, 30, 31	⊢
	: , : , :
27	instantiation	32, 33, 34, 35	⊢
	: , : , : , :
28	instantiation	36, 79, 37	⊢
	: , :
29	theorem		⊢
	proveit.logic.equality.sub_right_side_into
30	instantiation	38, 52, 53, 39, 40	⊢
	: , : , : , : , :
31	instantiation	59, 41, 42	⊢
	: , : , :
32	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
33	instantiation	69, 43	⊢
	: , : , :
34	instantiation	69, 44	⊢
	: , : , :
35	instantiation	78, 53	⊢
	:
36	theorem		⊢
	proveit.numbers.multiplication.commutation
37	instantiation	105, 81, 45	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_numer_left
39	instantiation	46, 79, 47	⊢
	:
40	instantiation	105, 48, 49	⊢
	: , : , :
41	instantiation	69, 50	⊢
	: , : , :
42	instantiation	69, 51	⊢
	: , : , :
43	instantiation	71, 52	⊢
	:
44	instantiation	71, 53	⊢
	:
45	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
46	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
47	instantiation	54, 55, 56	⊢
	: , :
48	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
49	instantiation	105, 57, 58	⊢
	: , : , :
50	instantiation	59, 60, 61	⊢
	: , : , :
51	instantiation	69, 62	⊢
	: , : , :
52	instantiation	105, 81, 63	⊢
	: , : , :
53	instantiation	105, 81, 64	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
55	instantiation	105, 67, 65	⊢
	: , : , :
56	instantiation	105, 67, 66	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
58	instantiation	105, 67, 68	⊢
	: , : , :
59	axiom		⊢
	proveit.logic.equality.equals_transitivity
60	instantiation	69, 70	⊢
	: , : , :
61	instantiation	71, 79	⊢
	:
62	instantiation	72, 79	⊢
	:
63	instantiation	105, 86, 73	⊢
	: , : , :
64	instantiation	105, 86, 74	⊢
	: , : , :
65	instantiation	105, 76, 75	⊢
	: , : , :
66	instantiation	105, 76, 104	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
68	instantiation	105, 76, 77	⊢
	: , : , :
69	axiom		⊢
	proveit.logic.equality.substitution
70	instantiation	78, 79	⊢
	:
71	theorem		⊢
	proveit.numbers.division.frac_one_denom
72	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
73	instantiation	105, 90, 101	⊢
	: , : , :
74	instantiation	105, 90, 80	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
76	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
77	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
78	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
79	instantiation	105, 81, 82	⊢
	: , : , :
80	instantiation	83, 84, 85	⊢
	: , : , :
81	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
82	instantiation	105, 86, 87	⊢
	: , : , :
83	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
84	instantiation	88, 89	⊢
	: , :
85	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_in_m_domain
86	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
87	instantiation	105, 90, 95	⊢
	: , : , :
88	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
89	instantiation	91, 92, 93	⊢
	: , :
90	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
91	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
92	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
93	instantiation	94, 95, 96	⊢
	: , :
94	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
95	instantiation	97, 98, 99	⊢
	: , :
96	instantiation	100, 101	⊢
	:
97	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
98	instantiation	105, 106, 102	⊢
	: , : , :
99	instantiation	105, 103, 104	⊢
	: , : , :
100	theorem		⊢
	proveit.numbers.negation.int_closure
101	instantiation	105, 106, 107	⊢
	: , : , :
102	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
103	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
104	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
105	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
106	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
107	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements