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_right_side_into
2	instantiation	4, 39	⊢
	:
3	modus ponens	5, 6	⊢
4	axiom		⊢
	proveit.physics.quantum.QPE._success_def
5	instantiation	7, 8, 9, 10*, 11*	⊢
	: , : , : , : , : , : , :
6	generalization	12	⊢
7	theorem		⊢
	proveit.statistics.complementary_event_prob_of_all
8	theorem		⊢
	proveit.physics.quantum.QPE._Omega_is_sample_space
9	theorem		⊢
	proveit.physics.quantum.QPE._sample_space_bijection
10	instantiation	13, 14	⊢
	: , :
11	instantiation	15, 16, 17	,  ⊢
	: , : , :
12	axiom		⊢
	proveit.logic.booleans.true_axiom
13	theorem		⊢
	proveit.logic.equality.equals_reversal
14	instantiation	18, 39	⊢
	:
15	axiom		⊢
	proveit.logic.equality.equals_transitivity
16	instantiation	19, 20	,  ⊢
	: , : , :
17	instantiation	21, 22	⊢
	:
18	axiom		⊢
	proveit.physics.quantum.QPE._fail_def
19	axiom		⊢
	proveit.logic.equality.substitution
20	instantiation	23, 24, 25	,  ⊢
	: , :
21	axiom		⊢
	proveit.logic.booleans.eq_true_intro
22	instantiation	26	⊢
	:
23	theorem		⊢
	proveit.numbers.ordering.less_complement_is_greater_eq
24	instantiation	66, 45, 27	⊢
	: , : , :
25	instantiation	28, 29, 30, 31	⊢
	: , :
26	axiom		⊢
	proveit.logic.equality.equals_reflexivity
27	instantiation	66, 51, 32	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.modular.mod_abs_real_closure
29	instantiation	33, 34, 35	⊢
	: , :
30	instantiation	66, 45, 36	⊢
	: , : , :
31	instantiation	37, 63	⊢
	:
32	instantiation	66, 38, 39	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
34	instantiation	66, 45, 40	⊢
	: , : , :
35	instantiation	41, 42	⊢
	:
36	instantiation	66, 51, 60	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
38	instantiation	55, 65, 43	⊢
	: , :
39	assumption		⊢
40	instantiation	66, 51, 44	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.negation.real_closure
42	instantiation	66, 45, 46	⊢
	: , : , :
43	instantiation	59, 47, 48	⊢
	: , :
44	instantiation	66, 49, 50	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
46	instantiation	66, 51, 52	⊢
	: , : , :
47	instantiation	66, 62, 53	⊢
	: , : , :
48	instantiation	64, 54	⊢
	:
49	instantiation	55, 56, 57	⊢
	: , :
50	assumption		⊢
51	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
52	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
53	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
54	instantiation	66, 67, 58	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
56	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
57	instantiation	59, 60, 61	⊢
	: , :
58	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
59	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
60	instantiation	66, 62, 63	⊢
	: , : , :
61	instantiation	64, 65	⊢
	:
62	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
63	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
64	theorem		⊢
	proveit.numbers.negation.int_closure
65	instantiation	66, 67, 68	⊢
	: , : , :
66	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
67	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
68	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements