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, one
from proveit.physics.quantum import NumKet, ket0
from proveit.physics.quantum.algebra import n_bit_interval

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(k, Conditional(Equals(NumKet(k, Add(n, one)), TensorProd(ket0, 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 k \rangle_{n + 1} = \left(\lvert 0 \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: 30 body: 3
2	ExprTuple	30
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	30, 12
10	Operation	operator: 25 operands: 13
11	Operation	operator: 14 operands: 15
12	Operation	operator: 16 operands: 17
13	ExprTuple	30, 18
14	Literal
15	ExprTuple	19, 20
16	Literal
17	ExprTuple	29, 21
18	Operation	operator: 27 operands: 22
19	Operation	operator: 23 operand: 29
20	Operation	operator: 25 operands: 26
21	Operation	operator: 27 operands: 28
22	ExprTuple	38, 39
23	Literal
24	ExprTuple	29
25	Literal
26	ExprTuple	30, 38
27	Literal
28	ExprTuple	31, 32
29	Literal
30	Variable
31	Operation	operator: 33 operands: 34
32	Operation	operator: 35 operand: 39
33	Literal
34	ExprTuple	37, 38
35	Literal
36	ExprTuple	39
37	Literal
38	Variable
39	Literal