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