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 ExprRange, ExprTuple, Variable
from proveit.core_expr_types import Len
from proveit.numbers import Add, Mult, four, one
from proveit.physics.quantum.QPE import _s, _t

# build up the expression from sub-expressions
sub_expr1 = Variable("_b", latex_format = r"{_{-}b}")
sub_expr2 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr3 = Add(_t, _s)
expr = ExprTuple(Mult(four, sub_expr3), Len(operands = [ExprRange(sub_expr1, ExprRange(sub_expr2, [sub_expr1, sub_expr2], one, sub_expr3), one, four)]))

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(4 \cdot \left(t + s\right), |\left(\left(1, 1\right), \left(1, 2\right), \ldots, \left(1, t + s\right), \left(2, 1\right), \left(2, 2\right), \ldots, \left(2, t + s\right), \ldots\ldots, \left(4, 1\right), \left(4, 2\right), \ldots, \left(4, t + s\right)\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: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	9, 14
5	Literal
6	ExprTuple	7
7	ExprRange	lambda_map: 8 start_index: 13 end_index: 9
8	Lambda	parameter: 19 body: 11
9	Literal
10	ExprTuple	19
11	ExprRange	lambda_map: 12 start_index: 13 end_index: 14
12	Lambda	parameter: 20 body: 16
13	Literal
14	Operation	operator: 17 operands: 18
15	ExprTuple	20
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	21, 22
19	Variable
20	Variable
21	Literal
22	Literal