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, l
from proveit.logic import And, InSet, TRUE
from proveit.numbers import Abs, Exp, two
from proveit.physics.quantum.QPE import _pos_domain, _rel_indexed_alpha

# build up the expression from sub-expressions
sub_expr1 = Exp(Abs(_rel_indexed_alpha), two)
sub_expr2 = InSet(l, _pos_domain)
expr = ExprTuple(Conditional(sub_expr1, And(sub_expr2, TRUE)), Conditional(sub_expr1, sub_expr2))

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(\left|\alpha_{b_{\textit{f}} \oplus l}\right|^{2} \textrm{ if } l \in \{e + 1~\ldotp \ldotp~2^{t - 1}\} ,  \top, \left|\alpha_{b_{\textit{f}} \oplus l}\right|^{2} \textrm{ if } l \in \{e + 1~\ldotp \ldotp~2^{t - 1}\}\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	Conditional	value: 4 condition: 3
2	Conditional	value: 4 condition: 8
3	Operation	operator: 5 operands: 6
4	Operation	operator: 25 operands: 7
5	Literal
6	ExprTuple	8, 9
7	ExprTuple	10, 30
8	Operation	operator: 11 operands: 12
9	Literal
10	Operation	operator: 13 operand: 16
11	Literal
12	ExprTuple	33, 15
13	Literal
14	ExprTuple	16
15	Operation	operator: 17 operands: 18
16	Operation	operator: 19 operand: 23
17	Literal
18	ExprTuple	21, 22
19	Literal
20	ExprTuple	23
21	Operation	operator: 34 operands: 24
22	Operation	operator: 25 operands: 26
23	Operation	operator: 27 operands: 28
24	ExprTuple	29, 40
25	Literal
26	ExprTuple	30, 31
27	Literal
28	ExprTuple	32, 33
29	Variable
30	Literal
31	Operation	operator: 34 operands: 35
32	Literal
33	Variable
34	Literal
35	ExprTuple	36, 37
36	Literal
37	Operation	operator: 38 operand: 40
38	Literal
39	ExprTuple	40
40	Literal