Expression of type ExprTuple

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, ExprTuple, Lambda, X, i, n
from proveit.core_expr_types import x_1_to_n, 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 = ExprTuple(Lambda([x_1_to_n], 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(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(x_{1}, x_{2}, \ldots, x_{n}\right) \mapsto \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(\mathcal{H}\right)\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 2 body: 3
2	ExprTuple	4
3	Conditional	value: 5 condition: 6
4	ExprRange	lambda_map: 7 start_index: 48 end_index: 49
5	Operation	operator: 8 operands: 9
6	Operation	operator: 34 operands: 10
7	Lambda	parameter: 50 body: 40
8	Literal
9	ExprTuple	11, 12
10	ExprTuple	13, 14
11	Operation	operator: 15 operands: 16
12	Operation	operator: 17 operand: 24
13	Operation	operator: 19 operands: 20
14	Operation	operator: 21 operand: 26
15	Literal
16	ExprTuple	26, 23
17	Literal
18	ExprTuple	24
19	Literal
20	ExprTuple	25
21	Literal
22	ExprTuple	26
23	Variable
24	Lambda	parameter: 53 body: 27
25	ExprRange	lambda_map: 28 start_index: 48 end_index: 49
26	Variable
27	Conditional	value: 29 condition: 30
28	Lambda	parameter: 50 body: 31
29	Operation	operator: 32 operands: 33
30	Operation	operator: 34 operands: 35
31	Operation	operator: 41 operand: 40
32	Literal
33	ExprTuple	37, 38
34	Literal
35	ExprTuple	53, 39
36	ExprTuple	40
37	Operation	operator: 41 operand: 47
38	Operation	operator: 42 operand: 47
39	Operation	operator: 44 operands: 45
40	IndexedVar	variable: 51 index: 50
41	Literal
42	Literal
43	ExprTuple	47
44	Literal
45	ExprTuple	48, 49
46	ExprTuple	50
47	IndexedVar	variable: 51 index: 53
48	Literal
49	Variable
50	Variable
51	Variable
52	ExprTuple	53
53	Variable