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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 m
from proveit.logic import Equals, Forall
from proveit.physics.quantum import NumBra, Qmult
from proveit.physics.quantum.QPE import _Psi_ket, _alpha_m, _m_domain, _t
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [m], instance_expr = Equals(_alpha_m, Qmult(NumBra(m, _t), _Psi_ket)), domain = _m_domain)
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_{m \in \{0~\ldotp \ldotp~2^{t} - 1\}}~\left(\alpha_{m} = \left({_{t}}\langle m \rvert \thinspace \lvert \Psi \rangle\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: 1
operand: 3
1Literal
2ExprTuple3
3Lambdaparameter: 28
body: 4
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operands: 8
6Operationoperator: 9
operands: 10
7Literal
8ExprTuple11, 12
9Literal
10ExprTuple28, 13
11Operationoperator: 14
operand: 28
12Operationoperator: 16
operands: 17
13Operationoperator: 18
operands: 19
14Literal
15ExprTuple28
16Literal
17ExprTuple20, 21
18Literal
19ExprTuple22, 23
20Operationoperator: 24
operands: 25
21Literal
22Literal
23Operationoperator: 26
operands: 27
24Literal
25ExprTuple28, 36
26Literal
27ExprTuple29, 30
28Variable
29Operationoperator: 31
operands: 32
30Operationoperator: 33
operand: 37
31Literal
32ExprTuple35, 36
33Literal
34ExprTuple37
35Literal
36Literal
37Literal