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, Forall, InSet
from proveit.numbers import Interval, NaturalPos, 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(n, Conditional(Forall(instance_param_or_params = [x_1_to_n], instance_expr = Equals(OrthoProj(Hspace, X), VecSum(index_or_indices = [i], summand = Qmult(Ket(x_i), Bra(x_i)), domain = Interval(one, n))), condition = InSet(x_1_to_n_kets, OrthoNormBases(Hspace))).with_wrapping(), InSet(n, NaturalPos))))

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(n \mapsto \left\{\begin{array}{l}\forall_{x_{1}, x_{2}, \ldots, x_{n}~|~\left\{\lvert x_{1} \rangle, \lvert x_{2} \rangle, \ldots, \lvert x_{n} \rangle\right\} \in \textrm{O.N.Bases}\left(\mathcal{H}\right)}~\\
\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)\right)\end{array} \textrm{ if } n \in \mathbb{N}^+\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	parameter: 58 body: 3
2	ExprTuple	58
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 43 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	58, 10
9	Lambda	parameters: 11 body: 12
10	Literal
11	ExprTuple	13
12	Conditional	value: 14 condition: 15
13	ExprRange	lambda_map: 16 start_index: 57 end_index: 58
14	Operation	operator: 17 operands: 18
15	Operation	operator: 43 operands: 19
16	Lambda	parameter: 59 body: 49
17	Literal
18	ExprTuple	20, 21
19	ExprTuple	22, 23
20	Operation	operator: 24 operands: 25
21	Operation	operator: 26 operand: 33
22	Operation	operator: 28 operands: 29
23	Operation	operator: 30 operand: 35
24	Literal
25	ExprTuple	35, 32
26	Literal
27	ExprTuple	33
28	Literal
29	ExprTuple	34
30	Literal
31	ExprTuple	35
32	Variable
33	Lambda	parameter: 62 body: 36
34	ExprRange	lambda_map: 37 start_index: 57 end_index: 58
35	Variable
36	Conditional	value: 38 condition: 39
37	Lambda	parameter: 59 body: 40
38	Operation	operator: 41 operands: 42
39	Operation	operator: 43 operands: 44
40	Operation	operator: 50 operand: 49
41	Literal
42	ExprTuple	46, 47
43	Literal
44	ExprTuple	62, 48
45	ExprTuple	49
46	Operation	operator: 50 operand: 56
47	Operation	operator: 51 operand: 56
48	Operation	operator: 53 operands: 54
49	IndexedVar	variable: 60 index: 59
50	Literal
51	Literal
52	ExprTuple	56
53	Literal
54	ExprTuple	57, 58
55	ExprTuple	59
56	IndexedVar	variable: 60 index: 62
57	Literal
58	Variable
59	Variable
60	Variable
61	ExprTuple	62
62	Variable