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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 Forall, InSet
from proveit.numbers import Exp, Real, frac, one, two
from proveit.physics.quantum.QPE import _diff_l_scaled_delta_floor, _pos_domain
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [l], instance_expr = InSet(frac(one, Exp(_diff_l_scaled_delta_floor, two)), Real), domain = _pos_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 \{e + 1~\ldotp \ldotp~2^{t - 1}\}}~\left(\frac{1}{\left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}} \in \mathbb{R}\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: 30
body: 5
4ExprTuple30
5Conditionalvalue: 6
condition: 7
6Operationoperator: 9
operands: 8
7Operationoperator: 9
operands: 10
8ExprTuple11, 12
9Literal
10ExprTuple30, 13
11Operationoperator: 14
operands: 15
12Literal
13Operationoperator: 16
operands: 17
14Literal
15ExprTuple37, 18
16Literal
17ExprTuple19, 20
18Operationoperator: 42
operands: 21
19Operationoperator: 28
operands: 22
20Operationoperator: 42
operands: 23
21ExprTuple24, 46
22ExprTuple25, 37
23ExprTuple46, 26
24Operationoperator: 28
operands: 27
25Variable
26Operationoperator: 28
operands: 29
27ExprTuple30, 31
28Literal
29ExprTuple47, 32
30Variable
31Operationoperator: 34
operand: 36
32Operationoperator: 34
operand: 37
33ExprTuple36
34Literal
35ExprTuple37
36Operationoperator: 38
operands: 39
37Literal
38Literal
39ExprTuple40, 41
40Operationoperator: 42
operands: 43
41Operationoperator: 44
operand: 48
42Literal
43ExprTuple46, 47
44Literal
45ExprTuple48
46Literal
47Literal
48Literal