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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 t
from proveit.linear_algebra import Norm
from proveit.logic import And, CartExp, Equals, Forall, InSet
from proveit.numbers import Complex, NaturalPos, one
from proveit.physics.quantum.QPE import _psi_t_ket, two_pow_t
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [t], instance_expr = And(InSet(_psi_t_ket, CartExp(Complex, two_pow_t)), Equals(Norm(_psi_t_ket), one)), 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_{t \in \mathbb{N}^+}~\left(\left(\lvert \psi_{t} \rangle \in \mathbb{C}^{2^{t}}\right) \land \left(\left \|\lvert \psi_{t} \rangle\right \| = 1\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: 32
body: 4
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operands: 8
6Operationoperator: 13
operands: 9
7Literal
8ExprTuple10, 11
9ExprTuple32, 12
10Operationoperator: 13
operands: 14
11Operationoperator: 15
operands: 16
12Literal
13Literal
14ExprTuple26, 17
15Literal
16ExprTuple18, 19
17Operationoperator: 20
operands: 21
18Operationoperator: 22
operand: 26
19Literal
20Literal
21ExprTuple24, 25
22Literal
23ExprTuple26
24Literal
25Operationoperator: 27
operands: 28
26Operationoperator: 29
operand: 32
27Literal
28ExprTuple31, 32
29Literal
30ExprTuple32
31Literal
32Variable