Expression of type Equals

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 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 Equals
from proveit.numbers import BinarySequence, one
from proveit.physics.quantum import Ket, NumKet

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Equals(NumKet(BinarySequence(a_1_to_k), k), TensorProd(ExprRange(sub_expr1, Ket(IndexedVar(a, sub_expr1)), 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())

\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)

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 18
7	Literal
8	ExprTuple	10
9	Operation	operator: 11 operands: 12
10	ExprRange	lambda_map: 13 start_index: 17 end_index: 18
11	Literal
12	ExprTuple	14
13	Lambda	parameter: 24 body: 15
14	ExprRange	lambda_map: 16 start_index: 17 end_index: 18
15	Operation	operator: 19 operand: 21
16	Lambda	parameter: 24 body: 21
17	Literal
18	Variable
19	Literal
20	ExprTuple	21
21	IndexedVar	variable: 22 index: 24
22	Variable
23	ExprTuple	24
24	Variable