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, Variable
from proveit.linear_algebra import InnerProd, ScalarMult
from proveit.numbers import Exp, Mult, Neg, e, i, pi, two, zero
from proveit.physics.quantum import ket0, ket1
from proveit.physics.quantum.QPE import _phase

# build up the expression from sub-expressions
sub_expr1 = Exp(e, Mult(two, pi, i, Exp(two, Neg(Variable("_a", latex_format = r"{_{-}a}"))), _phase))
expr = ExprTuple(ScalarMult(sub_expr1, InnerProd(ket0, ket1)), ScalarMult(sub_expr1, zero))

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(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{-{_{-}a}} \cdot \varphi} \cdot \left \langle \lvert 0 \rangle, \lvert 1 \rangle\right \rangle, \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{-{_{-}a}} \cdot \varphi} \cdot 0\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	7, 6
4	Literal
5	ExprTuple	7, 20
6	Operation	operator: 8 operands: 9
7	Operation	operator: 26 operands: 10
8	Literal
9	ExprTuple	11, 12
10	ExprTuple	13, 14
11	Operation	operator: 16 operand: 20
12	Operation	operator: 16 operand: 21
13	Literal
14	Operation	operator: 18 operands: 19
15	ExprTuple	20
16	Literal
17	ExprTuple	21
18	Literal
19	ExprTuple	28, 22, 23, 24, 25
20	Literal
21	Literal
22	Literal
23	Literal
24	Operation	operator: 26 operands: 27
25	Literal
26	Literal
27	ExprTuple	28, 29
28	Literal
29	Operation	operator: 30 operand: 32
30	Literal
31	ExprTuple	32
32	Variable