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	53	⊢
2	instantiation	3, 4	⊢
	: , :
3	theorem		⊢
	proveit.physics.quantum.circuits.prob_eq_via_equiv
4	modus ponens	5, 6	⊢
5	instantiation	7, 131, 134, 95, 8, 97	⊢
	: , : , : , : , : , : , : , :
6	instantiation	9, 10, 11, 93, 52, 12, 13, 14, 15, 16, 17, 18, 19, 20, 48, 95, 21, 22, 23, 45*	⊢
	: , : , : , : , : , :
7	theorem		⊢
	proveit.physics.quantum.circuits.circuit_equiv_temporal_sub
8	instantiation	108	⊢
	: , :
9	theorem		⊢
	proveit.physics.quantum.circuits.output_consolidation
10	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
11	instantiation	108	⊢
	: , :
12	instantiation	108	⊢
	: , :
13	instantiation	24, 25	⊢
	: , :
14	axiom		⊢
	proveit.physics.quantum.QPE._u_ket_register
15	instantiation	31, 26, 27, 28	⊢
	: , : , : , :
16	instantiation	53, 29	⊢
	: , :
17	instantiation	108	⊢
	: , :
18	instantiation	53, 30	⊢
	: , :
19	instantiation	31, 32, 33, 34	⊢
	: , : , : , :
20	instantiation	61, 90, 121, 45	⊢
	: , : , :
21	instantiation	132, 79, 93	⊢
	: , : , :
22	instantiation	132, 79, 35	⊢
	: , : , :
23	instantiation	36, 86, 37, 38, 39, 40	⊢
	: , :
24	theorem		⊢
	proveit.logic.booleans.conjunction.left_from_and
25	instantiation	41, 93	⊢
	:
26	instantiation	42	⊢
	: , : , :
27	instantiation	55	⊢
	:
28	instantiation	53, 43	⊢
	: , :
29	instantiation	44, 47, 45	⊢
	: , : , :
30	instantiation	46, 47, 48	⊢
	: , : , :
31	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
32	instantiation	49	⊢
	: , :
33	instantiation	55	⊢
	:
34	instantiation	53, 50	⊢
	: , :
35	instantiation	51, 93, 52	⊢
	: , :
36	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_all
37	instantiation	103	⊢
	: , : , :
38	instantiation	55	⊢
	:
39	instantiation	53, 54	⊢
	: , :
40	instantiation	55	⊢
	:
41	theorem		⊢
	proveit.physics.quantum.QPE._psi_t_ket_is_normalized_vec
42	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3
43	instantiation	62, 56, 57	⊢
	: , : , :
44	theorem		⊢
	proveit.core_expr_types.tuples.partition_front
45	instantiation	65, 121	⊢
	:
46	theorem		⊢
	proveit.core_expr_types.tuples.partition_back
47	instantiation	58, 59, 60	⊢
	:
48	instantiation	61, 121, 119, 106	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2
50	instantiation	62, 63, 64	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
52	axiom		⊢
	proveit.physics.quantum.QPE._s_in_nat_pos
53	theorem		⊢
	proveit.logic.equality.equals_reversal
54	instantiation	65, 66	⊢
	:
55	axiom		⊢
	proveit.logic.equality.equals_reflexivity
56	instantiation	74, 67	⊢
	: , : , :
57	instantiation	104, 68, 69	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
59	instantiation	70, 128, 71	⊢
	: , :
60	instantiation	72, 73	⊢
	: , :
61	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
62	theorem		⊢
	proveit.logic.equality.sub_right_side_into
63	instantiation	74, 75	⊢
	: , : , :
64	instantiation	104, 76, 77	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.addition.elim_zero_left
66	instantiation	132, 123, 78	⊢
	: , : , :
67	instantiation	132, 79, 80	⊢
	: , : , :
68	instantiation	113, 118	⊢
	: , : , :
69	instantiation	88, 95, 131, 134, 97, 81, 119, 90, 121, 82*	⊢
	: , : , : , : , : , :
70	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
71	instantiation	109, 83, 111	⊢
	: , : , :
72	theorem		⊢
	proveit.numbers.addition.subtraction.nonneg_difference
73	instantiation	84, 131	⊢
	:
74	theorem		⊢
	proveit.core_expr_types.tuples.range_len
75	instantiation	85, 86, 87, 134, 98	⊢
	: , :
76	instantiation	113, 118	⊢
	: , : , :
77	instantiation	88, 95, 131, 134, 97, 89, 121, 90, 91*	⊢
	: , : , : , : , : , :
78	instantiation	109, 92, 93	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
80	instantiation	94, 131, 95, 96, 97, 98, 134, 99	⊢
	: , : , : , : , :
81	instantiation	108	⊢
	: , :
82	instantiation	104, 100, 101	⊢
	: , : , :
83	instantiation	115, 102	⊢
	: , :
84	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
85	theorem		⊢
	proveit.numbers.addition.add_nat_closure
86	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
87	instantiation	103	⊢
	: , : , :
88	theorem		⊢
	proveit.numbers.addition.association
89	instantiation	108	⊢
	: , :
90	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
91	instantiation	104, 105, 106	⊢
	: , : , :
92	instantiation	115, 107	⊢
	: , :
93	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
94	theorem		⊢
	proveit.numbers.addition.add_nat_pos_from_nonneg
95	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
96	instantiation	108	⊢
	: , :
97	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
98	instantiation	109, 110, 111	⊢
	: , : , :
99	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
100	instantiation	113, 112	⊢
	: , : , :
101	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_1
102	theorem		⊢
	proveit.numbers.number_sets.integers.zero_set_within_int
103	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
104	axiom		⊢
	proveit.logic.equality.equals_transitivity
105	instantiation	113, 114	⊢
	: , : , :
106	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
107	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
108	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
109	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
110	instantiation	115, 116	⊢
	: , :
111	instantiation	117, 118	⊢
	: , :
112	instantiation	120, 119	⊢
	:
113	axiom		⊢
	proveit.logic.equality.substitution
114	instantiation	120, 121	⊢
	:
115	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
116	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.zero_set_within_nat
117	theorem		⊢
	proveit.logic.sets.enumeration.fold_singleton
118	theorem		⊢
	proveit.numbers.negation.negated_zero
119	instantiation	132, 123, 122	⊢
	: , : , :
120	theorem		⊢
	proveit.numbers.addition.elim_zero_right
121	instantiation	132, 123, 124	⊢
	: , : , :
122	instantiation	132, 126, 125	⊢
	: , : , :
123	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
124	instantiation	132, 126, 127	⊢
	: , : , :
125	instantiation	132, 129, 128	⊢
	: , : , :
126	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
127	instantiation	132, 129, 130	⊢
	: , : , :
128	instantiation	132, 133, 131	⊢
	: , : , :
129	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
130	instantiation	132, 133, 134	⊢
	: , : , :
131	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
132	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
133	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
134	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements