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