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, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20*	⊢
	: , : , : , : , : , :
1	theorem		⊢
	proveit.physics.quantum.circuits.input_consolidation
2	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
3	instantiation	104	⊢
	: , :
4	reference	89	⊢
5	reference	48	⊢
6	instantiation	104	⊢
	: , :
7	instantiation	21, 22	⊢
	: , :
8	axiom		⊢
	proveit.physics.quantum.QPE._u_ket_register
9	instantiation	28, 23, 24, 25	⊢
	: , : , : , :
10	instantiation	49, 26	⊢
	: , :
11	instantiation	104	⊢
	: , :
12	instantiation	49, 27	⊢
	: , :
13	instantiation	28, 29, 30, 31	⊢
	: , : , : , :
14	instantiation	57, 86, 117, 41	⊢
	: , : , :
15	reference	44	⊢
16	reference	91	⊢
17	instantiation	128, 75, 89	⊢
	: , : , :
18	instantiation	128, 75, 32	⊢
	: , : , :
19	instantiation	33, 82, 34, 35, 36, 37	⊢
	: , :
20	reference	41	⊢
21	theorem		⊢
	proveit.logic.booleans.conjunction.left_from_and
22	theorem		⊢
	proveit.physics.quantum.QPE._Psi_ket_is_normalized_vec
23	instantiation	38	⊢
	: , : , :
24	instantiation	51	⊢
	:
25	instantiation	49, 39	⊢
	: , :
26	instantiation	40, 43, 41	⊢
	: , : , :
27	instantiation	42, 43, 44	⊢
	: , : , :
28	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
29	instantiation	45	⊢
	: , :
30	instantiation	51	⊢
	:
31	instantiation	49, 46	⊢
	: , :
32	instantiation	47, 89, 48	⊢
	: , :
33	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_all
34	instantiation	99	⊢
	: , : , :
35	instantiation	51	⊢
	:
36	instantiation	49, 50	⊢
	: , :
37	instantiation	51	⊢
	:
38	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3
39	instantiation	58, 52, 53	⊢
	: , : , :
40	theorem		⊢
	proveit.core_expr_types.tuples.partition_front
41	instantiation	61, 117	⊢
	:
42	theorem		⊢
	proveit.core_expr_types.tuples.partition_back
43	instantiation	54, 55, 56	⊢
	:
44	instantiation	57, 117, 115, 102	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2
46	instantiation	58, 59, 60	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
48	axiom		⊢
	proveit.physics.quantum.QPE._s_in_nat_pos
49	theorem		⊢
	proveit.logic.equality.equals_reversal
50	instantiation	61, 62	⊢
	:
51	axiom		⊢
	proveit.logic.equality.equals_reflexivity
52	instantiation	70, 63	⊢
	: , : , :
53	instantiation	100, 64, 65	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
55	instantiation	66, 124, 67	⊢
	: , :
56	instantiation	68, 69	⊢
	: , :
57	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
58	theorem		⊢
	proveit.logic.equality.sub_right_side_into
59	instantiation	70, 71	⊢
	: , : , :
60	instantiation	100, 72, 73	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.addition.elim_zero_left
62	instantiation	128, 119, 74	⊢
	: , : , :
63	instantiation	128, 75, 76	⊢
	: , : , :
64	instantiation	109, 114	⊢
	: , : , :
65	instantiation	84, 91, 127, 130, 93, 77, 115, 86, 117, 78*	⊢
	: , : , : , : , : , :
66	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
67	instantiation	105, 79, 107	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.addition.subtraction.nonneg_difference
69	instantiation	80, 127	⊢
	:
70	theorem		⊢
	proveit.core_expr_types.tuples.range_len
71	instantiation	81, 82, 83, 130, 94	⊢
	: , :
72	instantiation	109, 114	⊢
	: , : , :
73	instantiation	84, 91, 127, 130, 93, 85, 117, 86, 87*	⊢
	: , : , : , : , : , :
74	instantiation	105, 88, 89	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
76	instantiation	90, 127, 91, 92, 93, 94, 130, 95	⊢
	: , : , : , : , :
77	instantiation	104	⊢
	: , :
78	instantiation	100, 96, 97	⊢
	: , : , :
79	instantiation	111, 98	⊢
	: , :
80	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
81	theorem		⊢
	proveit.numbers.addition.add_nat_closure
82	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
83	instantiation	99	⊢
	: , : , :
84	theorem		⊢
	proveit.numbers.addition.association
85	instantiation	104	⊢
	: , :
86	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
87	instantiation	100, 101, 102	⊢
	: , : , :
88	instantiation	111, 103	⊢
	: , :
89	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
90	theorem		⊢
	proveit.numbers.addition.add_nat_pos_from_nonneg
91	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
92	instantiation	104	⊢
	: , :
93	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
94	instantiation	105, 106, 107	⊢
	: , : , :
95	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
96	instantiation	109, 108	⊢
	: , : , :
97	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_1
98	theorem		⊢
	proveit.numbers.number_sets.integers.zero_set_within_int
99	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
100	axiom		⊢
	proveit.logic.equality.equals_transitivity
101	instantiation	109, 110	⊢
	: , : , :
102	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
103	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
104	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
105	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
106	instantiation	111, 112	⊢
	: , :
107	instantiation	113, 114	⊢
	: , :
108	instantiation	116, 115	⊢
	:
109	axiom		⊢
	proveit.logic.equality.substitution
110	instantiation	116, 117	⊢
	:
111	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
112	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.zero_set_within_nat
113	theorem		⊢
	proveit.logic.sets.enumeration.fold_singleton
114	theorem		⊢
	proveit.numbers.negation.negated_zero
115	instantiation	128, 119, 118	⊢
	: , : , :
116	theorem		⊢
	proveit.numbers.addition.elim_zero_right
117	instantiation	128, 119, 120	⊢
	: , : , :
118	instantiation	128, 122, 121	⊢
	: , : , :
119	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
120	instantiation	128, 122, 123	⊢
	: , : , :
121	instantiation	128, 125, 124	⊢
	: , : , :
122	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
123	instantiation	128, 125, 126	⊢
	: , : , :
124	instantiation	128, 129, 127	⊢
	: , : , :
125	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
126	instantiation	128, 129, 130	⊢
	: , : , :
127	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
128	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
129	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
130	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements