Expression of type Lambda

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, Lambda, i, n
from proveit.core_expr_types import x_i
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 = Lambda(i, Conditional(Qmult(Ket(x_i), Bra(x_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())

i \mapsto \left\{\lvert x_{i} \rangle \thinspace \langle x_{i} \rvert \textrm{ if } i \in \{1~\ldotp \ldotp~n\}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 21 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	21, 10
8	Operation	operator: 11 operand: 16
9	Operation	operator: 12 operand: 16
10	Operation	operator: 14 operands: 15
11	Literal
12	Literal
13	ExprTuple	16
14	Literal
15	ExprTuple	17, 18
16	IndexedVar	variable: 19 index: 21
17	Literal
18	Variable
19	Variable
20	ExprTuple	21
21	Variable