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