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, i, n
from proveit.core_expr_types import x_i
from proveit.linear_algebra import Hspace, Identity, OrthoNormBases, VecSum
from proveit.logic import Equals, InSet
from proveit.numbers import Interval, one
from proveit.physics.quantum import Bra, Ket, Qmult
from proveit.physics.quantum.algebra import x_1_to_n_kets

# build up the expression from sub-expressions
expr = Conditional(Equals(VecSum(index_or_indices = [i], summand = Qmult(Ket(x_i), Bra(x_i)), domain = Interval(one, n)), Identity(Hspace)), InSet(x_1_to_n_kets, OrthoNormBases(Hspace)))

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(\sum_{i=1}^{n} \left(\lvert x_{i} \rangle \thinspace \langle x_{i} \rvert\right)\right) = I_{\mathcal{H}} \textrm{ if } \left\{\lvert x_{1} \rangle, \lvert x_{2} \rangle, \ldots, \lvert x_{n} \rangle\right\} \in \textrm{O.N.Bases}\left(\mathcal{H}\right)\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: 27 operands: 5
3	Literal
4	ExprTuple	6, 7
5	ExprTuple	8, 9
6	Operation	operator: 10 operand: 17
7	Operation	operator: 12 operand: 19
8	Operation	operator: 13 operands: 14
9	Operation	operator: 15 operand: 19
10	Literal
11	ExprTuple	17
12	Literal
13	Literal
14	ExprTuple	18
15	Literal
16	ExprTuple	19
17	Lambda	parameter: 46 body: 20
18	ExprRange	lambda_map: 21 start_index: 41 end_index: 42
19	Variable
20	Conditional	value: 22 condition: 23
21	Lambda	parameter: 43 body: 24
22	Operation	operator: 25 operands: 26
23	Operation	operator: 27 operands: 28
24	Operation	operator: 34 operand: 33
25	Literal
26	ExprTuple	30, 31
27	Literal
28	ExprTuple	46, 32
29	ExprTuple	33
30	Operation	operator: 34 operand: 40
31	Operation	operator: 35 operand: 40
32	Operation	operator: 37 operands: 38
33	IndexedVar	variable: 44 index: 43
34	Literal
35	Literal
36	ExprTuple	40
37	Literal
38	ExprTuple	41, 42
39	ExprTuple	43
40	IndexedVar	variable: 44 index: 46
41	Literal
42	Variable
43	Variable
44	Variable
45	ExprTuple	46
46	Variable