Show the Proof¶

In [1]:
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

Out[1]:
step typerequirementsstatement
0instantiation1, 2
: , :
1theorem
proveit.physics.quantum.circuits.prob_eq_via_equiv
2modus ponens3, 4
3instantiation5, 92, 131, 128, 94, 6
: , : , : , : , : , : , : , :
4instantiation7, 8, 9, 90, 49, 10, 11, 12, 13, 14, 15, 16, 17, 18, 45, 92, 19, 20, 21, 42*
: , : , : , : , : , :
5theorem
proveit.physics.quantum.circuits.circuit_equiv_temporal_sub
6instantiation105
: , :
7theorem
proveit.physics.quantum.circuits.input_consolidation
8theorem
proveit.numbers.numerals.decimals.posnat2
9instantiation105
: , :
10instantiation105
: , :
11instantiation22, 23
: , :
12axiom
proveit.physics.quantum.QPE._u_ket_register
13instantiation29, 24, 25, 26
: , : , : , :
14instantiation50, 27
: , :
15instantiation105
: , :
16instantiation50, 28
: , :
17instantiation29, 30, 31, 32
: , : , : , :
18instantiation58, 87, 118, 42
: , : , :
19instantiation129, 76, 90
: , : , :
20instantiation129, 76, 33
: , : , :
21instantiation34, 83, 35, 36, 37, 38
: , :
22theorem
proveit.logic.booleans.conjunction.left_from_and
23theorem
proveit.physics.quantum.QPE._Psi_ket_is_normalized_vec
24instantiation39
: , : , :
25instantiation52
:
26instantiation50, 40
: , :
27instantiation41, 44, 42
: , : , :
28instantiation43, 44, 45
: , : , :
29theorem
proveit.logic.equality.four_chain_transitivity
30instantiation46
: , :
31instantiation52
:
32instantiation50, 47
: , :
33instantiation48, 90, 49
: , :
34theorem
proveit.logic.booleans.conjunction.and_if_all
35instantiation100
: , : , :
36instantiation52
:
37instantiation50, 51
: , :
38instantiation52
:
39theorem
proveit.numbers.numerals.decimals.tuple_len_3
40instantiation59, 53, 54
: , : , :
41theorem
proveit.core_expr_types.tuples.partition_front
42instantiation62, 118
:
43theorem
proveit.core_expr_types.tuples.partition_back
44instantiation55, 56, 57
:
45instantiation58, 118, 116, 103
: , : , :
46theorem
proveit.numbers.numerals.decimals.tuple_len_2
47instantiation59, 60, 61
: , : , :
48theorem
49axiom
proveit.physics.quantum.QPE._s_in_nat_pos
50theorem
proveit.logic.equality.equals_reversal
51instantiation62, 63
:
52axiom
proveit.logic.equality.equals_reflexivity
53instantiation71, 64
: , : , :
54instantiation101, 65, 66
: , : , :
55theorem
proveit.numbers.number_sets.integers.nonneg_int_is_natural
56instantiation67, 125, 68
: , :
57instantiation69, 70
: , :
58theorem
59theorem
proveit.logic.equality.sub_right_side_into
60instantiation71, 72
: , : , :
61instantiation101, 73, 74
: , : , :
62theorem
63instantiation129, 120, 75
: , : , :
64instantiation129, 76, 77
: , : , :
65instantiation110, 115
: , : , :
66instantiation85, 92, 128, 131, 94, 78, 116, 87, 118, 79*
: , : , : , : , : , :
67theorem
68instantiation106, 80, 108
: , : , :
69theorem
70instantiation81, 128
:
71theorem
proveit.core_expr_types.tuples.range_len
72instantiation82, 83, 84, 131, 95
: , :
73instantiation110, 115
: , : , :
74instantiation85, 92, 128, 131, 94, 86, 118, 87, 88*
: , : , : , : , : , :
75instantiation106, 89, 90
: , : , :
76theorem
proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
77instantiation91, 128, 92, 93, 94, 95, 131, 96
: , : , : , : , :
78instantiation105
: , :
79instantiation101, 97, 98
: , : , :
80instantiation112, 99
: , :
81theorem
proveit.numbers.number_sets.natural_numbers.natural_lower_bound
82theorem
83theorem
proveit.numbers.numerals.decimals.nat3
84instantiation100
: , : , :
85theorem
86instantiation105
: , :
87theorem
proveit.numbers.number_sets.complex_numbers.zero_is_complex
88instantiation101, 102, 103
: , : , :
89instantiation112, 104
: , :
90axiom
proveit.physics.quantum.QPE._t_in_natural_pos
91theorem
92axiom
proveit.numbers.number_sets.natural_numbers.zero_in_nats
93instantiation105
: , :
94theorem
proveit.core_expr_types.tuples.tuple_len_0_typical_eq
95instantiation106, 107, 108
: , : , :
96theorem
proveit.numbers.numerals.decimals.less_0_1
97instantiation110, 109
: , : , :
98theorem
99theorem
proveit.numbers.number_sets.integers.zero_set_within_int
100theorem
proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
101axiom
proveit.logic.equality.equals_transitivity
102instantiation110, 111
: , : , :
103theorem
104theorem
proveit.numbers.number_sets.real_numbers.nat_pos_within_real
105theorem
proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
106theorem
proveit.logic.sets.inclusion.unfold_subset_eq
107instantiation112, 113
: , :
108instantiation114, 115
: , :
109instantiation117, 116
:
110axiom
proveit.logic.equality.substitution
111instantiation117, 118
:
112theorem
proveit.logic.sets.inclusion.relax_proper_subset
113theorem
proveit.numbers.number_sets.natural_numbers.zero_set_within_nat
114theorem
proveit.logic.sets.enumeration.fold_singleton
115theorem
proveit.numbers.negation.negated_zero
116instantiation129, 120, 119
: , : , :
117theorem
118instantiation129, 120, 121
: , : , :
119instantiation129, 123, 122
: , : , :
120theorem
proveit.numbers.number_sets.complex_numbers.real_within_complex
121instantiation129, 123, 124
: , : , :
122instantiation129, 126, 125
: , : , :
123theorem
proveit.numbers.number_sets.real_numbers.rational_within_real
124instantiation129, 126, 127
: , : , :
125instantiation129, 130, 128
: , : , :
126theorem
proveit.numbers.number_sets.rational_numbers.int_within_rational
127instantiation129, 130, 131
: , : , :
128theorem
proveit.numbers.numerals.decimals.nat2
129theorem
proveit.logic.sets.inclusion.superset_membership_from_proper_subset
130theorem
proveit.numbers.number_sets.integers.nat_within_int
131theorem
proveit.numbers.numerals.decimals.nat1
*equality replacement requirements