Expression of type ExprTuple

from the theory of proveit.physics.quantum.circuits

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, IndexedVar, U, Variable, t
from proveit.linear_algebra import MatrixMult, ScalarMult
from proveit.logic import Equals
from proveit.numbers import Exp, Mult, e, i, one, pi, two
from proveit.physics.quantum import var_ket_u, varphi

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(ExprRange(sub_expr1, Equals(MatrixMult(IndexedVar(U, sub_expr1), var_ket_u), ScalarMult(Exp(e, Mult(two, pi, i, IndexedVar(varphi, sub_expr1))), var_ket_u)), one, t))

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(\left(U_{1} \thinspace \lvert u \rangle\right) = \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi_{1}} \cdot \lvert u \rangle\right)\right), \left(\left(U_{2} \thinspace \lvert u \rangle\right) = \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi_{2}} \cdot \lvert u \rangle\right)\right), \ldots, \left(\left(U_{t} \thinspace \lvert u \rangle\right) = \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi_{t}} \cdot \lvert u \rangle\right)\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	ExprRange	lambda_map: 2 start_index: 3 end_index: 4
2	Lambda	parameter: 30 body: 5
3	Literal
4	Variable
5	Operation	operator: 6 operands: 7
6	Literal
7	ExprTuple	8, 9
8	Operation	operator: 10 operands: 11
9	Operation	operator: 12 operands: 13
10	Literal
11	ExprTuple	14, 16
12	Literal
13	ExprTuple	15, 16
14	IndexedVar	variable: 17 index: 30
15	Operation	operator: 18 operands: 19
16	Variable
17	Variable
18	Literal
19	ExprTuple	20, 21
20	Literal
21	Operation	operator: 22 operands: 23
22	Literal
23	ExprTuple	24, 25, 26, 27
24	Literal
25	Literal
26	Literal
27	IndexedVar	variable: 28 index: 30
28	Variable
29	ExprTuple	30
30	Variable