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Expression of type Forall

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.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import U, n
from proveit.linear_algebra import Unitary
from proveit.logic import CartExp, Forall, InSet
from proveit.numbers import Complex, NaturalPos
from proveit.physics.quantum import Qmult, var_ket_psi
In [2]:
# build up the expression from sub-expressions
sub_expr1 = CartExp(Complex, n)
expr = Forall(instance_param_or_params = [n], instance_expr = Forall(instance_param_or_params = [U], instance_expr = Forall(instance_param_or_params = [var_ket_psi], instance_expr = InSet(Qmult(U, var_ket_psi), sub_expr1), domain = sub_expr1), domain = Unitary(n)), 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_{U \in \textrm{U}\left(n\right)}~\left[\forall_{\lvert \psi \rangle \in \mathbb{C}^{n}}~\left(\left(U \thinspace \lvert \psi \rangle\right) \in \mathbb{C}^{n}\right)\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: 14
operand: 2
1ExprTuple2
2Lambdaparameter: 37
body: 3
3Conditionalvalue: 4
condition: 5
4Operationoperator: 14
operand: 8
5Operationoperator: 26
operands: 7
6ExprTuple8
7ExprTuple37, 9
8Lambdaparameter: 34
body: 11
9Literal
10ExprTuple34
11Conditionalvalue: 12
condition: 13
12Operationoperator: 14
operand: 17
13Operationoperator: 26
operands: 16
14Literal
15ExprTuple17
16ExprTuple34, 18
17Lambdaparameter: 35
body: 20
18Operationoperator: 21
operand: 37
19ExprTuple35
20Conditionalvalue: 23
condition: 24
21Literal
22ExprTuple37
23Operationoperator: 26
operands: 25
24Operationoperator: 26
operands: 27
25ExprTuple28, 29
26Literal
27ExprTuple35, 29
28Operationoperator: 30
operands: 31
29Operationoperator: 32
operands: 33
30Literal
31ExprTuple34, 35
32Literal
33ExprTuple36, 37
34Variable
35Variable
36Literal
37Variable