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	generalization	1	⊢
1	instantiation	2, 3, 4	⊢
	: , : , :
2	theorem		⊢
	proveit.logic.equality.sub_right_side_into
3	instantiation	5, 40	⊢
	:
4	modus ponens	6, 7	⊢
5	axiom		⊢
	proveit.physics.quantum.QPE._success_def
6	instantiation	8, 9, 10, 11*, 12*	⊢
	: , : , : , : , : , : , :
7	generalization	13	⊢
8	theorem		⊢
	proveit.statistics.complementary_event_prob_of_all
9	theorem		⊢
	proveit.physics.quantum.QPE._Omega_is_sample_space
10	theorem		⊢
	proveit.physics.quantum.QPE._sample_space_bijection
11	instantiation	14, 15	⊢
	: , :
12	instantiation	16, 17, 18	,  ⊢
	: , : , :
13	axiom		⊢
	proveit.logic.booleans.true_axiom
14	theorem		⊢
	proveit.logic.equality.equals_reversal
15	instantiation	19, 40	⊢
	:
16	axiom		⊢
	proveit.logic.equality.equals_transitivity
17	instantiation	20, 21	,  ⊢
	: , : , :
18	instantiation	22, 23	⊢
	:
19	axiom		⊢
	proveit.physics.quantum.QPE._fail_def
20	axiom		⊢
	proveit.logic.equality.substitution
21	instantiation	24, 25, 26	,  ⊢
	: , :
22	axiom		⊢
	proveit.logic.booleans.eq_true_intro
23	instantiation	27	⊢
	:
24	theorem		⊢
	proveit.numbers.ordering.less_complement_is_greater_eq
25	instantiation	67, 46, 28	⊢
	: , : , :
26	instantiation	29, 30, 31, 32	⊢
	: , :
27	axiom		⊢
	proveit.logic.equality.equals_reflexivity
28	instantiation	67, 52, 33	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.modular.mod_abs_real_closure
30	instantiation	34, 35, 36	⊢
	: , :
31	instantiation	67, 46, 37	⊢
	: , : , :
32	instantiation	38, 64	⊢
	:
33	instantiation	67, 39, 40	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
35	instantiation	67, 46, 41	⊢
	: , : , :
36	instantiation	42, 43	⊢
	:
37	instantiation	67, 52, 61	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
39	instantiation	56, 66, 44	⊢
	: , :
40	assumption		⊢
41	instantiation	67, 52, 45	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.negation.real_closure
43	instantiation	67, 46, 47	⊢
	: , : , :
44	instantiation	60, 48, 49	⊢
	: , :
45	instantiation	67, 50, 51	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
47	instantiation	67, 52, 53	⊢
	: , : , :
48	instantiation	67, 63, 54	⊢
	: , : , :
49	instantiation	65, 55	⊢
	:
50	instantiation	56, 57, 58	⊢
	: , :
51	assumption		⊢
52	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
53	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
54	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
55	instantiation	67, 68, 59	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
57	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
58	instantiation	60, 61, 62	⊢
	: , :
59	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
60	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
61	instantiation	67, 63, 64	⊢
	: , : , :
62	instantiation	65, 66	⊢
	:
63	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
64	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
65	theorem		⊢
	proveit.numbers.negation.int_closure
66	instantiation	67, 68, 69	⊢
	: , : , :
67	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
68	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
69	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements