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, 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(VecSum(index_or_indices = [i], summand = Qmult(Ket(x_i), Bra(x_i)), domain = Interval(one, n)), Identity(Hspace)), 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(\left(\sum_{i=1}^{n} \left(\lvert x_{i} \rangle \thinspace \langle x_{i} \rvert\right)\right) = I_{\mathcal{H}}\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: 56 body: 3
2	ExprTuple	56
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 41 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	56, 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: 55 end_index: 56
14	Operation	operator: 17 operands: 18
15	Operation	operator: 41 operands: 19
16	Lambda	parameter: 57 body: 47
17	Literal
18	ExprTuple	20, 21
19	ExprTuple	22, 23
20	Operation	operator: 24 operand: 31
21	Operation	operator: 26 operand: 33
22	Operation	operator: 27 operands: 28
23	Operation	operator: 29 operand: 33
24	Literal
25	ExprTuple	31
26	Literal
27	Literal
28	ExprTuple	32
29	Literal
30	ExprTuple	33
31	Lambda	parameter: 60 body: 34
32	ExprRange	lambda_map: 35 start_index: 55 end_index: 56
33	Variable
34	Conditional	value: 36 condition: 37
35	Lambda	parameter: 57 body: 38
36	Operation	operator: 39 operands: 40
37	Operation	operator: 41 operands: 42
38	Operation	operator: 48 operand: 47
39	Literal
40	ExprTuple	44, 45
41	Literal
42	ExprTuple	60, 46
43	ExprTuple	47
44	Operation	operator: 48 operand: 54
45	Operation	operator: 49 operand: 54
46	Operation	operator: 51 operands: 52
47	IndexedVar	variable: 58 index: 57
48	Literal
49	Literal
50	ExprTuple	54
51	Literal
52	ExprTuple	55, 56
53	ExprTuple	57
54	IndexedVar	variable: 58 index: 60
55	Literal
56	Variable
57	Variable
58	Variable
59	ExprTuple	60
60	Variable