Expression of type Lambda

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, 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 = 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(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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 20 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10
8	Operation	operator: 11 operands: 12
9	Operation	operator: 13 operands: 14
10	ExprRange	lambda_map: 15 start_index: 28 end_index: 29
11	Literal
12	ExprTuple	16, 29
13	Literal
14	ExprTuple	17
15	Lambda	parameter: 35 body: 18
16	Operation	operator: 19 operands: 20
17	ExprRange	lambda_map: 21 start_index: 28 end_index: 29
18	Operation	operator: 22 operands: 23
19	Literal
20	ExprTuple	24
21	Lambda	parameter: 35 body: 25
22	Literal
23	ExprTuple	32, 26
24	ExprRange	lambda_map: 27 start_index: 28 end_index: 29
25	Operation	operator: 30 operand: 32
26	Literal
27	Lambda	parameter: 35 body: 32
28	Literal
29	Variable
30	Literal
31	ExprTuple	32
32	IndexedVar	variable: 33 index: 35
33	Variable
34	ExprTuple	35
35	Variable