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