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Expression of type Forall

from the theory of proveit.physics.quantum.QPE

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.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import k
from proveit.linalg import TensorExp
from proveit.logic import Forall, InSet
from proveit.numbers import Complex, Exp, NaturalPos, two
from proveit.physics.quantum import Ket
from proveit.physics.quantum.QPE import psi_k
In [2]:
# build up the expression from sub-expressions
expr = Forall([k], InSet(Ket(psi_k), TensorExp([Exp(Complex, two)], k)), domain = NaturalPos)
Out[2]:
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(expr.latex())
\forall_{k \in \mathbb{N}^+}~\left(\lvert \psi_{k} \rangle \in \left(\mathbb{C}^{2}\right)^{\otimes k}\right)
In [5]:
expr.style_options()
Out[5]:
namedescriptiondefaultcurrent valuerelated methods
with_wrappingIf 'True', wrap the Expression after the parametersNoneNone/False('with_wrapping',)
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
expr.expr_info()
Out[6]:
 core typesub-expressionsexpression
0Operationoperator: 1
operand: 3
1Literal
2ExprTuple3
3Lambdaparameter: 23
body: 4
4Conditionalvalue: 5
condition: 6
5Operationoperator: 8
operands: 7
6Operationoperator: 8
operands: 9
7ExprTuple10, 11
8Literal
9ExprTuple23, 12
10Operationoperator: 13
operand: 17
11Operationoperator: 15
operands: 16
12Literal
13Literal
14ExprTuple17
15Literal
16ExprTuple18, 23
17Operationoperator: 19
operands: 20
18ExprTuple21
19Literal
20ExprTuple22, 23
21Operationoperator: 24
operands: 25
22Literal
23Variable
24Literal
25ExprTuple26, 27
26Literal
27Literal