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