Expression of type ExprTuple

from the theory of proveit.physics.quantum.QPE

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import ExprRange, ExprTuple, IndexedVar, Variable, a, c, k, m
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Complex, Exp, Mult, Neg, Sum, e, frac, i, one, pi, two, zero
from proveit.physics.quantum.QPE import _m_domain, _phase, _two_pow_t

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = [k]
sub_expr3 = IndexedVar(a, one)
sub_expr4 = ExprRange(sub_expr1, IndexedVar(c, sub_expr1), one, zero)
sub_expr5 = Mult(Exp(e, Mult(two, pi, i, _phase, k)), Exp(e, Neg(frac(Mult(two, pi, i, k, m), _two_pow_t))))
expr = ExprTuple(Forall(instance_param_or_params = sub_expr2, instance_expr = InSet(sub_expr5, Complex), domain = _m_domain), Forall(instance_param_or_params = [sub_expr3, sub_expr4], instance_expr = Equals(Mult(sub_expr3, Sum(index_or_indices = sub_expr2, summand = sub_expr5, domain = _m_domain), sub_expr4), Sum(index_or_indices = sub_expr2, summand = Mult(sub_expr3, sub_expr5, sub_expr4), domain = _m_domain)).with_wrapping_at(2), domain = Complex).with_wrapping())

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(\forall_{k \in \{0~\ldotp \ldotp~2^{t} - 1\}}~\left(\left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \mathsf{e}^{-\frac{2 \cdot \pi \cdot \mathsf{i} \cdot k \cdot m}{2^{t}}}\right) \in \mathbb{C}\right), \begin{array}{l}\forall_{a_{1}, c_{1}, c_{2}, \ldots, c_{0} \in \mathbb{C}}~\\
\left(\begin{array}{c} \begin{array}{l} \left(a_{1} \cdot \left(\sum_{k = 0}^{2^{t} - 1} \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \mathsf{e}^{-\frac{2 \cdot \pi \cdot \mathsf{i} \cdot k \cdot m}{2^{t}}}\right)\right)\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{0}\right) =  \\ \left(\sum_{k = 0}^{2^{t} - 1} \left(a_{1} \cdot \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \mathsf{e}^{-\frac{2 \cdot \pi \cdot \mathsf{i} \cdot k \cdot m}{2^{t}}}\right)\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{0}\right)\right) \end{array} \end{array}\right)\end{array}\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 4 operand: 6
2	Operation	operator: 4 operand: 7
3	ExprTuple	6
4	Literal
5	ExprTuple	7
6	Lambda	parameter: 85 body: 8
7	Lambda	parameters: 9 body: 10
8	Conditional	value: 11 condition: 40
9	ExprTuple	41, 43
10	Conditional	value: 12 condition: 13
11	Operation	operator: 44 operands: 14
12	Operation	operator: 15 operands: 16
13	Operation	operator: 17 operands: 18
14	ExprTuple	42, 36
15	Literal
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	21, 22
19	Operation	operator: 79 operands: 23
20	Operation	operator: 30 operand: 28
21	Operation	operator: 44 operands: 25
22	ExprRange	lambda_map: 26 start_index: 76 end_index: 59
23	ExprTuple	41, 27, 43
24	ExprTuple	28
25	ExprTuple	41, 36
26	Lambda	parameter: 64 body: 29
27	Operation	operator: 30 operand: 34
28	Lambda	parameter: 85 body: 32
29	Operation	operator: 44 operands: 33
30	Literal
31	ExprTuple	34
32	Conditional	value: 35 condition: 40
33	ExprTuple	52, 36
34	Lambda	parameter: 85 body: 38
35	Operation	operator: 79 operands: 39
36	Literal
37	ExprTuple	85
38	Conditional	value: 42 condition: 40
39	ExprTuple	41, 42, 43
40	Operation	operator: 44 operands: 45
41	IndexedVar	variable: 46 index: 76
42	Operation	operator: 79 operands: 47
43	ExprRange	lambda_map: 48 start_index: 76 end_index: 59
44	Literal
45	ExprTuple	85, 49
46	Variable
47	ExprTuple	50, 51
48	Lambda	parameter: 64 body: 52
49	Operation	operator: 53 operands: 54
50	Operation	operator: 81 operands: 55
51	Operation	operator: 81 operands: 56
52	IndexedVar	variable: 57 index: 64
53	Literal
54	ExprTuple	59, 60
55	ExprTuple	62, 61
56	ExprTuple	62, 63
57	Variable
58	ExprTuple	64
59	Literal
60	Operation	operator: 65 operands: 66
61	Operation	operator: 79 operands: 67
62	Literal
63	Operation	operator: 72 operand: 71
64	Variable
65	Literal
66	ExprTuple	78, 69
67	ExprTuple	87, 83, 84, 70, 85
68	ExprTuple	71
69	Operation	operator: 72 operand: 76
70	Literal
71	Operation	operator: 74 operands: 75
72	Literal
73	ExprTuple	76
74	Literal
75	ExprTuple	77, 78
76	Literal
77	Operation	operator: 79 operands: 80
78	Operation	operator: 81 operands: 82
79	Literal
80	ExprTuple	87, 83, 84, 85, 86
81	Literal
82	ExprTuple	87, 88
83	Literal
84	Literal
85	Variable
86	Variable
87	Literal
88	Literal