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, ExprRange, ExprTuple, IndexedVar, Lambda, Variable, a, k
from proveit.core_expr_types import a_1_to_k
from proveit.linear_algebra import TensorProd
from proveit.logic import And, Equals, InSet
from proveit.numbers import BinarySequence, Bit, one
from proveit.physics.quantum import Ket, NumKet

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = IndexedVar(a, sub_expr1)
expr = ExprTuple(Lambda([a_1_to_k], Conditional(Equals(NumKet(BinarySequence(a_1_to_k), k), TensorProd(ExprRange(sub_expr1, Ket(sub_expr2), one, k))), And(ExprRange(sub_expr1, InSet(sub_expr2, Bit), one, k)))))

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(\left(a_{1}, a_{2}, \ldots, a_{k}\right) \mapsto \left\{\lvert \texttt{\#}\texttt{b}(a_{1}, a_{2}, \ldots, a_{k}) \rangle_{k} = \left(\lvert a_{1} \rangle {\otimes}  \lvert a_{2} \rangle {\otimes}  \ldots {\otimes}  \lvert a_{k} \rangle\right) \textrm{ if } \left(a_{1} \in \mathbb{N}^{\leq 1}\right) \land  \left(a_{2} \in \mathbb{N}^{\leq 1}\right) \land  \ldots \land  \left(a_{k} \in \mathbb{N}^{\leq 1}\right)\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	parameters: 21 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11
9	Operation	operator: 12 operands: 13
10	Operation	operator: 14 operands: 15
11	ExprRange	lambda_map: 16 start_index: 29 end_index: 30
12	Literal
13	ExprTuple	17, 30
14	Literal
15	ExprTuple	18
16	Lambda	parameter: 36 body: 19
17	Operation	operator: 20 operands: 21
18	ExprRange	lambda_map: 22 start_index: 29 end_index: 30
19	Operation	operator: 23 operands: 24
20	Literal
21	ExprTuple	25
22	Lambda	parameter: 36 body: 26
23	Literal
24	ExprTuple	33, 27
25	ExprRange	lambda_map: 28 start_index: 29 end_index: 30
26	Operation	operator: 31 operand: 33
27	Literal
28	Lambda	parameter: 36 body: 33
29	Literal
30	Variable
31	Literal
32	ExprTuple	33
33	IndexedVar	variable: 34 index: 36
34	Variable
35	ExprTuple	36
36	Variable