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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.linear_algebra import HilbertSpaces, Hspace
from proveit.logic import Forall, InClass, InSet
from proveit.physics.quantum import Qmult, QmultCodomain, bra_varphi, ket_varphi, varphi
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [Hspace], instance_expr = Forall(instance_param_or_params = [varphi], instance_expr = InClass(Qmult(bra_varphi), QmultCodomain), condition = InSet(ket_varphi, Hspace)), domain = HilbertSpaces)
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_{\mathcal{H} \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces}}~\left[\forall_{\varphi~|~\lvert \varphi \rangle \in \mathcal{H}}~\left(\left[\langle \varphi \rvert\right] \underset{{\scriptscriptstyle c}}{\in} \mathcal{Q^*}\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: 22
body: 4
3ExprTuple22
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operand: 10
6Operationoperator: 15
operands: 9
7Literal
8ExprTuple10
9ExprTuple22, 11
10Lambdaparameter: 29
body: 12
11Literal
12Conditionalvalue: 13
condition: 14
13Operationoperator: 15
operands: 16
14Operationoperator: 17
operands: 18
15Literal
16ExprTuple19, 20
17Literal
18ExprTuple21, 22
19Operationoperator: 23
operand: 26
20Literal
21Operationoperator: 25
operand: 29
22Variable
23Literal
24ExprTuple26
25Literal
26Operationoperator: 27
operand: 29
27Literal
28ExprTuple29
29Variable