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 ExprTuple, l
from proveit.logic import Forall, InSet
from proveit.numbers import Exp, Mult, Real, Sum, four, frac, one, two
from proveit.physics.quantum.QPE import _diff_l_scaled_delta_floor, _neg_domain

# build up the expression from sub-expressions
sub_expr1 = [l]
sub_expr2 = frac(one, Mult(four, Exp(_diff_l_scaled_delta_floor, two)))
expr = ExprTuple(Forall(instance_param_or_params = sub_expr1, instance_expr = InSet(sub_expr2, Real), domain = _neg_domain), InSet(Sum(index_or_indices = sub_expr1, summand = sub_expr2, domain = _neg_domain), Real))

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_{l \in \{-2^{t - 1} + 1~\ldotp \ldotp~-\left(e + 1\right)\}}~\left(\frac{1}{4 \cdot \left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}} \in \mathbb{R}\right), \left(\sum_{l = -2^{t - 1} + 1}^{-\left(e + 1\right)} \frac{1}{4 \cdot \left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}}\right) \in \mathbb{R}\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: 21 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 16
6	Lambda	parameter: 41 body: 8
7	Operation	operator: 9 operand: 12
8	Conditional	value: 11 condition: 18
9	Literal
10	ExprTuple	12
11	Operation	operator: 21 operands: 13
12	Lambda	parameter: 41 body: 15
13	ExprTuple	17, 16
14	ExprTuple	41
15	Conditional	value: 17 condition: 18
16	Literal
17	Operation	operator: 19 operands: 20
18	Operation	operator: 21 operands: 22
19	Literal
20	ExprTuple	65, 23
21	Literal
22	ExprTuple	41, 24
23	Operation	operator: 49 operands: 25
24	Operation	operator: 26 operands: 27
25	ExprTuple	28, 29
26	Literal
27	ExprTuple	30, 31
28	Literal
29	Operation	operator: 56 operands: 32
30	Operation	operator: 51 operands: 33
31	Operation	operator: 60 operand: 37
32	ExprTuple	35, 62
33	ExprTuple	36, 65
34	ExprTuple	37
35	Operation	operator: 51 operands: 38
36	Operation	operator: 60 operand: 43
37	Operation	operator: 51 operands: 40
38	ExprTuple	41, 42
39	ExprTuple	43
40	ExprTuple	44, 65
41	Variable
42	Operation	operator: 60 operand: 47
43	Operation	operator: 56 operands: 46
44	Variable
45	ExprTuple	47
46	ExprTuple	62, 48
47	Operation	operator: 49 operands: 50
48	Operation	operator: 51 operands: 52
49	Literal
50	ExprTuple	53, 54
51	Literal
52	ExprTuple	63, 55
53	Operation	operator: 56 operands: 57
54	Operation	operator: 58 operand: 64
55	Operation	operator: 60 operand: 65
56	Literal
57	ExprTuple	62, 63
58	Literal
59	ExprTuple	64
60	Literal
61	ExprTuple	65
62	Literal
63	Literal
64	Literal
65	Literal