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 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 = 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())

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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 38 body: 2
1	ExprTuple	38
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 31 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	38, 9
8	Lambda	parameters: 29 body: 10
9	Literal
10	Conditional	value: 11 condition: 12
11	Operation	operator: 13 operands: 14
12	Operation	operator: 15 operands: 16
13	Literal
14	ExprTuple	17, 18
15	Literal
16	ExprTuple	19
17	Operation	operator: 20 operands: 21
18	Operation	operator: 22 operands: 23
19	ExprRange	lambda_map: 24 start_index: 37 end_index: 38
20	Literal
21	ExprTuple	25, 38
22	Literal
23	ExprTuple	26
24	Lambda	parameter: 44 body: 27
25	Operation	operator: 28 operands: 29
26	ExprRange	lambda_map: 30 start_index: 37 end_index: 38
27	Operation	operator: 31 operands: 32
28	Literal
29	ExprTuple	33
30	Lambda	parameter: 44 body: 34
31	Literal
32	ExprTuple	41, 35
33	ExprRange	lambda_map: 36 start_index: 37 end_index: 38
34	Operation	operator: 39 operand: 41
35	Literal
36	Lambda	parameter: 44 body: 41
37	Literal
38	Variable
39	Literal
40	ExprTuple	41
41	IndexedVar	variable: 42 index: 44
42	Variable
43	ExprTuple	44
44	Variable