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, l
from proveit.logic import InSet
from proveit.numbers import IntervalCO, Neg, frac, one, subtract, two
from proveit.physics.quantum.QPE import _delta_b_floor, _full_domain, _two_pow_t

# build up the expression from sub-expressions
sub_expr1 = frac(one, two)
expr = ExprTuple(Lambda(l, Conditional(InSet(subtract(_delta_b_floor, frac(l, _two_pow_t)), IntervalCO(Neg(sub_expr1), sub_expr1)), InSet(l, _full_domain))))

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(l \mapsto \left\{\left(\delta_{b_{\textit{f}}} - \frac{l}{2^{t}}\right) \in \left[-\frac{1}{2},\frac{1}{2}\right) \textrm{ if } l \in \{-2^{t - 1} + 1~\ldotp \ldotp~2^{t - 1}\}\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 34 body: 3
2	ExprTuple	34
3	Conditional	value: 4 condition: 5
4	Operation	operator: 7 operands: 6
5	Operation	operator: 7 operands: 8
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	34, 11
9	Operation	operator: 42 operands: 12
10	Operation	operator: 13 operands: 14
11	Operation	operator: 15 operands: 16
12	ExprTuple	17, 18
13	Literal
14	ExprTuple	19, 28
15	Literal
16	ExprTuple	20, 36
17	Operation	operator: 21 operand: 26
18	Operation	operator: 46 operand: 27
19	Operation	operator: 46 operand: 28
20	Operation	operator: 42 operands: 25
21	Literal
22	ExprTuple	26
23	ExprTuple	27
24	ExprTuple	28
25	ExprTuple	29, 48
26	Literal
27	Operation	operator: 31 operands: 30
28	Operation	operator: 31 operands: 32
29	Operation	operator: 46 operand: 36
30	ExprTuple	34, 35
31	Literal
32	ExprTuple	48, 40
33	ExprTuple	36
34	Variable
35	Operation	operator: 38 operands: 37
36	Operation	operator: 38 operands: 39
37	ExprTuple	40, 44
38	Literal
39	ExprTuple	40, 41
40	Literal
41	Operation	operator: 42 operands: 43
42	Literal
43	ExprTuple	44, 45
44	Literal
45	Operation	operator: 46 operand: 48
46	Literal
47	ExprTuple	48
48	Literal