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	⊢
	: , :
1	reference	52	⊢
2	instantiation	3, 4	⊢
	: , :
3	theorem		⊢
	proveit.physics.quantum.circuits.prob_eq_via_equiv
4	modus ponens	5, 6	⊢
5	instantiation	7, 94, 133, 130, 96, 8	⊢
	: , : , : , : , : , : , : , :
6	instantiation	9, 10, 11, 92, 51, 12, 13, 14, 15, 16, 17, 18, 19, 20, 47, 94, 21, 22, 23, 44*	⊢
	: , : , : , : , : , :
7	theorem		⊢
	proveit.physics.quantum.circuits.circuit_equiv_temporal_sub
8	instantiation	107	⊢
	: , :
9	theorem		⊢
	proveit.physics.quantum.circuits.input_consolidation
10	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
11	instantiation	107	⊢
	: , :
12	instantiation	107	⊢
	: , :
13	instantiation	24, 25	⊢
	: , :
14	axiom		⊢
	proveit.physics.quantum.QPE._u_ket_register
15	instantiation	31, 26, 27, 28	⊢
	: , : , : , :
16	instantiation	52, 29	⊢
	: , :
17	instantiation	107	⊢
	: , :
18	instantiation	52, 30	⊢
	: , :
19	instantiation	31, 32, 33, 34	⊢
	: , : , : , :
20	instantiation	60, 89, 120, 44	⊢
	: , : , :
21	instantiation	131, 78, 92	⊢
	: , : , :
22	instantiation	131, 78, 35	⊢
	: , : , :
23	instantiation	36, 85, 37, 38, 39, 40	⊢
	: , :
24	theorem		⊢
	proveit.logic.booleans.conjunction.left_from_and
25	theorem		⊢
	proveit.physics.quantum.QPE._Psi_ket_is_normalized_vec
26	instantiation	41	⊢
	: , : , :
27	instantiation	54	⊢
	:
28	instantiation	52, 42	⊢
	: , :
29	instantiation	43, 46, 44	⊢
	: , : , :
30	instantiation	45, 46, 47	⊢
	: , : , :
31	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
32	instantiation	48	⊢
	: , :
33	instantiation	54	⊢
	:
34	instantiation	52, 49	⊢
	: , :
35	instantiation	50, 92, 51	⊢
	: , :
36	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_all
37	instantiation	102	⊢
	: , : , :
38	instantiation	54	⊢
	:
39	instantiation	52, 53	⊢
	: , :
40	instantiation	54	⊢
	:
41	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3
42	instantiation	61, 55, 56	⊢
	: , : , :
43	theorem		⊢
	proveit.core_expr_types.tuples.partition_front
44	instantiation	64, 120	⊢
	:
45	theorem		⊢
	proveit.core_expr_types.tuples.partition_back
46	instantiation	57, 58, 59	⊢
	:
47	instantiation	60, 120, 118, 105	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2
49	instantiation	61, 62, 63	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
51	axiom		⊢
	proveit.physics.quantum.QPE._s_in_nat_pos
52	theorem		⊢
	proveit.logic.equality.equals_reversal
53	instantiation	64, 65	⊢
	:
54	axiom		⊢
	proveit.logic.equality.equals_reflexivity
55	instantiation	73, 66	⊢
	: , : , :
56	instantiation	103, 67, 68	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
58	instantiation	69, 127, 70	⊢
	: , :
59	instantiation	71, 72	⊢
	: , :
60	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
61	theorem		⊢
	proveit.logic.equality.sub_right_side_into
62	instantiation	73, 74	⊢
	: , : , :
63	instantiation	103, 75, 76	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.addition.elim_zero_left
65	instantiation	131, 122, 77	⊢
	: , : , :
66	instantiation	131, 78, 79	⊢
	: , : , :
67	instantiation	112, 117	⊢
	: , : , :
68	instantiation	87, 94, 130, 133, 96, 80, 118, 89, 120, 81*	⊢
	: , : , : , : , : , :
69	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
70	instantiation	108, 82, 110	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.addition.subtraction.nonneg_difference
72	instantiation	83, 130	⊢
	:
73	theorem		⊢
	proveit.core_expr_types.tuples.range_len
74	instantiation	84, 85, 86, 133, 97	⊢
	: , :
75	instantiation	112, 117	⊢
	: , : , :
76	instantiation	87, 94, 130, 133, 96, 88, 120, 89, 90*	⊢
	: , : , : , : , : , :
77	instantiation	108, 91, 92	⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
79	instantiation	93, 130, 94, 95, 96, 97, 133, 98	⊢
	: , : , : , : , :
80	instantiation	107	⊢
	: , :
81	instantiation	103, 99, 100	⊢
	: , : , :
82	instantiation	114, 101	⊢
	: , :
83	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
84	theorem		⊢
	proveit.numbers.addition.add_nat_closure
85	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
86	instantiation	102	⊢
	: , : , :
87	theorem		⊢
	proveit.numbers.addition.association
88	instantiation	107	⊢
	: , :
89	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
90	instantiation	103, 104, 105	⊢
	: , : , :
91	instantiation	114, 106	⊢
	: , :
92	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
93	theorem		⊢
	proveit.numbers.addition.add_nat_pos_from_nonneg
94	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
95	instantiation	107	⊢
	: , :
96	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
97	instantiation	108, 109, 110	⊢
	: , : , :
98	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
99	instantiation	112, 111	⊢
	: , : , :
100	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_1
101	theorem		⊢
	proveit.numbers.number_sets.integers.zero_set_within_int
102	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
103	axiom		⊢
	proveit.logic.equality.equals_transitivity
104	instantiation	112, 113	⊢
	: , : , :
105	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
106	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
107	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
108	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
109	instantiation	114, 115	⊢
	: , :
110	instantiation	116, 117	⊢
	: , :
111	instantiation	119, 118	⊢
	:
112	axiom		⊢
	proveit.logic.equality.substitution
113	instantiation	119, 120	⊢
	:
114	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
115	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.zero_set_within_nat
116	theorem		⊢
	proveit.logic.sets.enumeration.fold_singleton
117	theorem		⊢
	proveit.numbers.negation.negated_zero
118	instantiation	131, 122, 121	⊢
	: , : , :
119	theorem		⊢
	proveit.numbers.addition.elim_zero_right
120	instantiation	131, 122, 123	⊢
	: , : , :
121	instantiation	131, 125, 124	⊢
	: , : , :
122	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
123	instantiation	131, 125, 126	⊢
	: , : , :
124	instantiation	131, 128, 127	⊢
	: , : , :
125	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
126	instantiation	131, 128, 129	⊢
	: , : , :
127	instantiation	131, 132, 130	⊢
	: , : , :
128	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
129	instantiation	131, 132, 133	⊢
	: , : , :
130	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
131	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
132	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
133	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements