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, ExprRange, ExprTuple, Variable
from proveit.core_expr_types import Len
from proveit.numbers import greater, greater_eq, one, subtract, two
from proveit.physics.quantum.QPE import _two_pow__t_minus_one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = subtract(_two_pow__t_minus_one, one)
expr = ExprTuple(Len(operands = [Conditional(_two_pow__t_minus_one, greater_eq(_two_pow__t_minus_one, sub_expr2)), Conditional(sub_expr2, greater(sub_expr2, _two_pow__t_minus_one))]), Len(operands = [ExprRange(sub_expr1, sub_expr1, one, two)]))

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(2^{t - 1} \textrm{ if } 2^{t - 1} \geq \left(2^{t - 1} - 1\right), 2^{t - 1} - 1 \textrm{ if } \left(2^{t - 1} - 1\right) > 2^{t - 1}\right)|, |\left(1, \ldots, 2\right)|\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 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	8
6	Conditional	value: 20 condition: 9
7	Conditional	value: 17 condition: 10
8	ExprRange	lambda_map: 11 start_index: 31 end_index: 23
9	Operation	operator: 12 operands: 13
10	Operation	operator: 14 operands: 15
11	Lambda	parameter: 18 body: 18
12	Literal
13	ExprTuple	17, 20
14	Literal
15	ExprTuple	20, 17
16	ExprTuple	18
17	Operation	operator: 25 operands: 19
18	Variable
19	ExprTuple	20, 28
20	Operation	operator: 21 operands: 22
21	Literal
22	ExprTuple	23, 24
23	Literal
24	Operation	operator: 25 operands: 26
25	Literal
26	ExprTuple	27, 28
27	Literal
28	Operation	operator: 29 operand: 31
29	Literal
30	ExprTuple	31
31	Literal