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, k, n
from proveit.linear_algebra import TensorProd
from proveit.logic import Equals, InSet
from proveit.numbers import Add, Exp, one, two
from proveit.physics.quantum import NumKet, ket1
from proveit.physics.quantum.algebra import n_bit_interval

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(k, Conditional(Equals(NumKet(Add(Exp(two, n), k), Add(n, one)), TensorProd(ket1, NumKet(k, n))), InSet(k, n_bit_interval))))

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(k \mapsto \left\{\lvert 2^{n} + k \rangle_{n + 1} = \left(\lvert 1 \rangle {\otimes} \lvert k \rangle_{n}\right) \textrm{ if } k \in \{0~\ldotp \ldotp~2^{n} - 1\}\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: 31 body: 3
2	ExprTuple	31
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	31, 12
10	Operation	operator: 27 operands: 13
11	Operation	operator: 14 operands: 15
12	Operation	operator: 16 operands: 17
13	ExprTuple	18, 19
14	Literal
15	ExprTuple	20, 21
16	Literal
17	ExprTuple	22, 23
18	Operation	operator: 29 operands: 24
19	Operation	operator: 29 operands: 25
20	Operation	operator: 26 operand: 40
21	Operation	operator: 27 operands: 28
22	Literal
23	Operation	operator: 29 operands: 30
24	ExprTuple	32, 31
25	ExprTuple	39, 40
26	Literal
27	Literal
28	ExprTuple	31, 39
29	Literal
30	ExprTuple	32, 33
31	Variable
32	Operation	operator: 34 operands: 35
33	Operation	operator: 36 operand: 40
34	Literal
35	ExprTuple	38, 39
36	Literal
37	ExprTuple	40
38	Literal
39	Variable
40	Literal