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 Equals, Forall, InSet
from proveit.numbers import BinarySequence, Bit, NaturalPos, one
from proveit.physics.quantum import Ket, NumKet

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

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\{\forall_{a_{1}, a_{2}, \ldots, a_{k} \in \mathbb{N}^{\leq 1}}~\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)\right) \textrm{ if } k \in \mathbb{N}^+\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: 39 body: 3
2	ExprTuple	39
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 32 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	39, 10
9	Lambda	parameters: 30 body: 11
10	Literal
11	Conditional	value: 12 condition: 13
12	Operation	operator: 14 operands: 15
13	Operation	operator: 16 operands: 17
14	Literal
15	ExprTuple	18, 19
16	Literal
17	ExprTuple	20
18	Operation	operator: 21 operands: 22
19	Operation	operator: 23 operands: 24
20	ExprRange	lambda_map: 25 start_index: 38 end_index: 39
21	Literal
22	ExprTuple	26, 39
23	Literal
24	ExprTuple	27
25	Lambda	parameter: 45 body: 28
26	Operation	operator: 29 operands: 30
27	ExprRange	lambda_map: 31 start_index: 38 end_index: 39
28	Operation	operator: 32 operands: 33
29	Literal
30	ExprTuple	34
31	Lambda	parameter: 45 body: 35
32	Literal
33	ExprTuple	42, 36
34	ExprRange	lambda_map: 37 start_index: 38 end_index: 39
35	Operation	operator: 40 operand: 42
36	Literal
37	Lambda	parameter: 45 body: 42
38	Literal
39	Variable
40	Literal
41	ExprTuple	42
42	IndexedVar	variable: 43 index: 45
43	Variable
44	ExprTuple	45
45	Variable