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