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