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Expression of type Conditional

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 Conditional, c
from proveit.linear_algebra import HilbertSpaces, Hspace
from proveit.logic import Forall, InSet
from proveit.numbers import Complex
from proveit.physics.quantum import Qmult, var_ket_psi
In [2]:
# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [Hspace], instance_expr = Forall(instance_param_or_params = [var_ket_psi], instance_expr = InSet(Qmult(c, var_ket_psi), Hspace), domain = Hspace), domain = HilbertSpaces), InSet(c, Complex))
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())
\left\{\forall_{\mathcal{H} \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces}}~\left[\forall_{\lvert \psi \rangle \in \mathcal{H}}~\left(\left(c \thinspace \lvert \psi \rangle\right) \in \mathcal{H}\right)\right] \textrm{ if } c \in \mathbb{C}\right..
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
condition_delimiter'comma' or 'and'commacomma('with_comma_delimiter', 'with_conjunction_delimiter')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 11
operand: 5
2Operationoperator: 22
operands: 4
3ExprTuple5
4ExprTuple28, 6
5Lambdaparameter: 25
body: 8
6Literal
7ExprTuple25
8Conditionalvalue: 9
condition: 10
9Operationoperator: 11
operand: 15
10Operationoperator: 13
operands: 14
11Literal
12ExprTuple15
13Literal
14ExprTuple25, 16
15Lambdaparameter: 29
body: 18
16Literal
17ExprTuple29
18Conditionalvalue: 19
condition: 20
19Operationoperator: 22
operands: 21
20Operationoperator: 22
operands: 23
21ExprTuple24, 25
22Literal
23ExprTuple29, 25
24Operationoperator: 26
operands: 27
25Variable
26Literal
27ExprTuple28, 29
28Variable
29Variable