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