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 Conditional, ExprTuple, Lambda, k, m
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Exp, Mod, Mult, Neg, e, frac, i, pi, two
from proveit.physics.quantum.QPE import _m_domain, _two_pow_t

# build up the expression from sub-expressions
sub_expr1 = Exp(e, Neg(frac(Mult(two, pi, i, k, m), _two_pow_t)))
sub_expr2 = InSet(k, _m_domain)
sub_expr3 = Exp(e, Neg(frac(Mult(two, pi, i, k, Mod(m, _two_pow_t)), _two_pow_t)))
expr = ExprTuple(Forall(instance_param_or_params = [k], instance_expr = Equals(sub_expr3, sub_expr1), domain = _m_domain), Equals(Lambda(k, Conditional(sub_expr3, sub_expr2)), Lambda(k, Conditional(sub_expr1, sub_expr2))).with_wrapping_at(2))

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(\mathsf{e}^{-\frac{2 \cdot \pi \cdot \mathsf{i} \cdot k \cdot \left(m ~\textup{mod}~ 2^{t}\right)}{2^{t}}} = \mathsf{e}^{-\frac{2 \cdot \pi \cdot \mathsf{i} \cdot k \cdot m}{2^{t}}}\right), \begin{array}{c} \begin{array}{l} \left[k \mapsto \left\{\mathsf{e}^{-\frac{2 \cdot \pi \cdot \mathsf{i} \cdot k \cdot \left(m ~\textup{mod}~ 2^{t}\right)}{2^{t}}} \textrm{ if } k \in \{0~\ldotp \ldotp~2^{t} - 1\}\right..\right] =  \\ \left[k \mapsto \left\{\mathsf{e}^{-\frac{2 \cdot \pi \cdot \mathsf{i} \cdot k \cdot m}{2^{t}}} \textrm{ if } k \in \{0~\ldotp \ldotp~2^{t} - 1\}\right..\right] \end{array} \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: 3 operand: 6
2	Operation	operator: 15 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8
6	Lambda	parameter: 52 body: 9
7	Lambda	parameter: 52 body: 10
8	Lambda	parameter: 52 body: 12
9	Conditional	value: 13 condition: 14
10	Conditional	value: 19 condition: 14
11	ExprTuple	52
12	Conditional	value: 20 condition: 14
13	Operation	operator: 15 operands: 16
14	Operation	operator: 17 operands: 18
15	Literal
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	52, 21
19	Operation	operator: 57 operands: 22
20	Operation	operator: 57 operands: 23
21	Operation	operator: 24 operands: 25
22	ExprTuple	27, 26
23	ExprTuple	27, 28
24	Literal
25	ExprTuple	29, 30
26	Operation	operator: 41 operand: 35
27	Literal
28	Operation	operator: 41 operand: 36
29	Literal
30	Operation	operator: 33 operands: 34
31	ExprTuple	35
32	ExprTuple	36
33	Literal
34	ExprTuple	56, 37
35	Operation	operator: 39 operands: 38
36	Operation	operator: 39 operands: 40
37	Operation	operator: 41 operand: 45
38	ExprTuple	43, 56
39	Literal
40	ExprTuple	44, 56
41	Literal
42	ExprTuple	45
43	Operation	operator: 47 operands: 46
44	Operation	operator: 47 operands: 48
45	Literal
46	ExprTuple	59, 50, 51, 52, 49
47	Literal
48	ExprTuple	59, 50, 51, 52, 55
49	Operation	operator: 53 operands: 54
50	Literal
51	Literal
52	Variable
53	Literal
54	ExprTuple	55, 56
55	Variable
56	Operation	operator: 57 operands: 58
57	Literal
58	ExprTuple	59, 60
59	Literal
60	Literal