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, Function, f, i, n
from proveit.core_expr_types import a_i, v_i
from proveit.linear_algebra import ScalarMult
from proveit.logic import InSet
from proveit.numbers import Interval, one
from proveit.physics.quantum import Bra, Ket, Qmult

# build up the expression from sub-expressions
expr = Conditional(ScalarMult(Function(f, [a_i]), Qmult(Ket(v_i), Bra(v_i))), InSet(i, Interval(one, n)))

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\{f\left(a_{i}\right) \cdot \left(\lvert v_{i} \rangle \thinspace \langle v_{i} \rvert\right) \textrm{ if } i \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	28, 9
7	Operation	operator: 10 operand: 16
8	Operation	operator: 12 operands: 13
9	Operation	operator: 14 operands: 15
10	Variable
11	ExprTuple	16
12	Literal
13	ExprTuple	17, 18
14	Literal
15	ExprTuple	19, 20
16	IndexedVar	variable: 21 index: 28
17	Operation	operator: 22 operand: 25
18	Operation	operator: 23 operand: 25
19	Literal
20	Variable
21	Variable
22	Literal
23	Literal
24	ExprTuple	25
25	IndexedVar	variable: 26 index: 28
26	Variable
27	ExprTuple	28
28	Variable