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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 l
from proveit.logic import Equals, Forall
from proveit.numbers import Abs, ModAbs
from proveit.physics.quantum.QPE import _full_domain, _two_pow_t
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [l], instance_expr = Equals(ModAbs(l, _two_pow_t), Abs(l)), domain = _full_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_{l \in \{-2^{t - 1} + 1~\ldotp \ldotp~2^{t - 1}\}}~\left(\left|l\right|_{\textup{mod}\thinspace 2^{t}} = \left|l\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: 21
body: 4
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operands: 8
6Operationoperator: 9
operands: 10
7Literal
8ExprTuple11, 12
9Literal
10ExprTuple21, 13
11Operationoperator: 14
operands: 15
12Operationoperator: 16
operand: 21
13Operationoperator: 18
operands: 19
14Literal
15ExprTuple21, 20
16Literal
17ExprTuple21
18Literal
19ExprTuple22, 27
20Operationoperator: 28
operands: 23
21Variable
22Operationoperator: 32
operands: 24
23ExprTuple30, 34
24ExprTuple25, 38
25Operationoperator: 36
operand: 27
26ExprTuple27
27Operationoperator: 28
operands: 29
28Literal
29ExprTuple30, 31
30Literal
31Operationoperator: 32
operands: 33
32Literal
33ExprTuple34, 35
34Literal
35Operationoperator: 36
operand: 38
36Literal
37ExprTuple38
38Literal