Expression of type ExprTuple

from the theory of proveit.physics.quantum.algebra

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, Lambda, U, i, j, n
from proveit.core_expr_types import v_i, v_j
from proveit.linear_algebra import Adj
from proveit.logic import And, Equals, InSet
from proveit.numbers import Interval, KroneckerDelta, one
from proveit.physics.quantum import Bra, Ket, Qmult

# build up the expression from sub-expressions
sub_expr1 = Interval(one, n)
expr = ExprTuple(Lambda([i, j], Conditional(Equals(Qmult(Bra(v_i), Adj(U), U, Ket(v_j)), KroneckerDelta(i, j)), And(InSet(i, sub_expr1), InSet(j, sub_expr1)))))

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(i, j\right) \mapsto \left\{\left(\langle v_{i} \rvert \thinspace U^{\dagger} \thinspace U \thinspace \lvert v_{j} \rangle\right) = \delta_{i, j} \textrm{ if } i \in \{1~\ldotp \ldotp~n\} ,  j \in \{1~\ldotp \ldotp~n\}\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	Lambda	parameters: 16 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12
9	Operation	operator: 13 operands: 14
10	Operation	operator: 15 operands: 16
11	Operation	operator: 18 operands: 17
12	Operation	operator: 18 operands: 19
13	Literal
14	ExprTuple	20, 21, 33, 22
15	Literal
16	ExprTuple	40, 41
17	ExprTuple	40, 23
18	Literal
19	ExprTuple	41, 23
20	Operation	operator: 24 operand: 32
21	Operation	operator: 26 operand: 33
22	Operation	operator: 28 operand: 34
23	Operation	operator: 30 operands: 31
24	Literal
25	ExprTuple	32
26	Literal
27	ExprTuple	33
28	Literal
29	ExprTuple	34
30	Literal
31	ExprTuple	35, 36
32	IndexedVar	variable: 38 index: 40
33	Variable
34	IndexedVar	variable: 38 index: 41
35	Literal
36	Variable
37	ExprTuple	40
38	Variable
39	ExprTuple	41
40	Variable
41	Variable