Expression of type Conditional

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, 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 = 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\{\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()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

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