# from the theory of proveit.physics.quantum.algebra¶

In [1]:
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.
# import Expression classes needed to build the expression
from proveit import j, k, n
from proveit.logic import Forall, NotEquals
from proveit.numbers import NaturalPos
from proveit.physics.quantum import NumKet
from proveit.physics.quantum.algebra import n_bit_interval

In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [n], instance_expr = Forall(instance_param_or_params = [j, k], instance_expr = NotEquals(NumKet(j, n), NumKet(k, n)), domain = n_bit_interval, condition = NotEquals(j, k)), domain = NaturalPos)

expr:
In [3]:
# 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

In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\forall_{n \in \mathbb{N}^+}~\left[\forall_{j, k \in \{0~\ldotp \ldotp~2^{n} - 1\}~|~j \neq k}~\left(\lvert j \rangle_{n} \neq \lvert k \rangle_{n}\right)\right]

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
with_wrappingIf 'True', wrap the Expression after the parametersNoneNone/False('with_wrapping',)
condition_wrappingWrap 'before' or 'after' the condition (or None).NoneNone/False('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_paramsIf 'True', wraps every two parameters AND wraps the Expression after the parametersNoneNone/False('with_params',)
justificationjustify to the 'left', 'center', or 'right' in the array cellscentercenter('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Operationoperator: 7
operand: 2
1ExprTuple2
2Lambdaparameter: 47
body: 4
3ExprTuple47
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operand: 10
6Operationoperator: 27
operands: 9
7Literal
8ExprTuple10
9ExprTuple47, 11
10Lambdaparameters: 30
body: 12
11Literal
12Conditionalvalue: 13
condition: 14
13Operationoperator: 29
operands: 15
14Operationoperator: 16
operands: 17
15ExprTuple18, 19
16Literal
17ExprTuple20, 21, 22
18Operationoperator: 24
operands: 23
19Operationoperator: 24
operands: 25
20Operationoperator: 27
operands: 26
21Operationoperator: 27
operands: 28
22Operationoperator: 29
operands: 30
23ExprTuple32, 47
24Literal
25ExprTuple33, 47
26ExprTuple32, 31
27Literal
28ExprTuple33, 31
29Literal
30ExprTuple32, 33
31Operationoperator: 34
operands: 35
32Variable
33Variable
34Literal
35ExprTuple36, 37
36Literal
37Operationoperator: 38
operands: 39
38Literal
39ExprTuple40, 41
40Operationoperator: 42
operands: 43
41Operationoperator: 44
operand: 48
42Literal
43ExprTuple46, 47
44Literal
45ExprTuple48
46Literal
47Variable
48Literal