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, i, n
from proveit.core_expr_types import x_1_to_n, 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 = ExprTuple(Lambda([x_1_to_n], 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(x_{1}, x_{2}, \ldots, x_{n}\right) \mapsto \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..\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: 46 end_index: 47
5	Operation	operator: 8 operands: 9
6	Operation	operator: 32 operands: 10
7	Lambda	parameter: 48 body: 38
8	Literal
9	ExprTuple	11, 12
10	ExprTuple	13, 14
11	Operation	operator: 15 operand: 22
12	Operation	operator: 17 operand: 24
13	Operation	operator: 18 operands: 19
14	Operation	operator: 20 operand: 24
15	Literal
16	ExprTuple	22
17	Literal
18	Literal
19	ExprTuple	23
20	Literal
21	ExprTuple	24
22	Lambda	parameter: 51 body: 25
23	ExprRange	lambda_map: 26 start_index: 46 end_index: 47
24	Variable
25	Conditional	value: 27 condition: 28
26	Lambda	parameter: 48 body: 29
27	Operation	operator: 30 operands: 31
28	Operation	operator: 32 operands: 33
29	Operation	operator: 39 operand: 38
30	Literal
31	ExprTuple	35, 36
32	Literal
33	ExprTuple	51, 37
34	ExprTuple	38
35	Operation	operator: 39 operand: 45
36	Operation	operator: 40 operand: 45
37	Operation	operator: 42 operands: 43
38	IndexedVar	variable: 49 index: 48
39	Literal
40	Literal
41	ExprTuple	45
42	Literal
43	ExprTuple	46, 47
44	ExprTuple	48
45	IndexedVar	variable: 49 index: 51
46	Literal
47	Variable
48	Variable
49	Variable
50	ExprTuple	51
51	Variable