Expression of type Conditional

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, 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 = 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(\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..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 10
7	Operation	operator: 11 operands: 12
8	Operation	operator: 13 operands: 14
9	Operation	operator: 16 operands: 15
10	Operation	operator: 16 operands: 17
11	Literal
12	ExprTuple	18, 19, 31, 20
13	Literal
14	ExprTuple	38, 39
15	ExprTuple	38, 21
16	Literal
17	ExprTuple	39, 21
18	Operation	operator: 22 operand: 30
19	Operation	operator: 24 operand: 31
20	Operation	operator: 26 operand: 32
21	Operation	operator: 28 operands: 29
22	Literal
23	ExprTuple	30
24	Literal
25	ExprTuple	31
26	Literal
27	ExprTuple	32
28	Literal
29	ExprTuple	33, 34
30	IndexedVar	variable: 36 index: 38
31	Variable
32	IndexedVar	variable: 36 index: 39
33	Literal
34	Variable
35	ExprTuple	38
36	Variable
37	ExprTuple	39
38	Variable
39	Variable