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, X, i, n
from proveit.core_expr_types import x_i
from proveit.linear_algebra import Hspace, OrthoNormBases, OrthoProj, 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(OrthoProj(Hspace, X), VecSum(index_or_indices = [i], summand = Qmult(Ket(x_i), Bra(x_i)), domain = Interval(one, n))), InSet(x_1_to_n_kets, OrthoNormBases(X)))

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\{\textrm{OrthoProj}\left(\mathcal{H}, X\right) = \left(\sum_{i=1}^{n} \left(\lvert x_{i} \rangle \thinspace \langle x_{i} \rvert\right)\right) \textrm{ if } \left\{\lvert x_{1} \rangle, \lvert x_{2} \rangle, \ldots, \lvert x_{n} \rangle\right\} \in \textrm{O.N.Bases}\left(X\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: 29 operands: 5
3	Literal
4	ExprTuple	6, 7
5	ExprTuple	8, 9
6	Operation	operator: 10 operands: 11
7	Operation	operator: 12 operand: 19
8	Operation	operator: 14 operands: 15
9	Operation	operator: 16 operand: 21
10	Literal
11	ExprTuple	18, 21
12	Literal
13	ExprTuple	19
14	Literal
15	ExprTuple	20
16	Literal
17	ExprTuple	21
18	Variable
19	Lambda	parameter: 48 body: 22
20	ExprRange	lambda_map: 23 start_index: 43 end_index: 44
21	Variable
22	Conditional	value: 24 condition: 25
23	Lambda	parameter: 45 body: 26
24	Operation	operator: 27 operands: 28
25	Operation	operator: 29 operands: 30
26	Operation	operator: 36 operand: 35
27	Literal
28	ExprTuple	32, 33
29	Literal
30	ExprTuple	48, 34
31	ExprTuple	35
32	Operation	operator: 36 operand: 42
33	Operation	operator: 37 operand: 42
34	Operation	operator: 39 operands: 40
35	IndexedVar	variable: 46 index: 45
36	Literal
37	Literal
38	ExprTuple	42
39	Literal
40	ExprTuple	43, 44
41	ExprTuple	45
42	IndexedVar	variable: 46 index: 48
43	Literal
44	Variable
45	Variable
46	Variable
47	ExprTuple	48
48	Variable