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_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 = 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(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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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