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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, _neg_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 = _neg_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~-\left(e + 1\right)\}}~\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
15ExprTuple54, 18
16Literal
17ExprTuple19, 20
18Operationoperator: 45
operands: 21
19Operationoperator: 40
operands: 22
20Operationoperator: 49
operand: 26
21ExprTuple24, 51
22ExprTuple25, 54
23ExprTuple26
24Operationoperator: 40
operands: 27
25Operationoperator: 49
operand: 32
26Operationoperator: 40
operands: 29
27ExprTuple30, 31
28ExprTuple32
29ExprTuple33, 54
30Variable
31Operationoperator: 49
operand: 36
32Operationoperator: 45
operands: 35
33Variable
34ExprTuple36
35ExprTuple51, 37
36Operationoperator: 38
operands: 39
37Operationoperator: 40
operands: 41
38Literal
39ExprTuple42, 43
40Literal
41ExprTuple52, 44
42Operationoperator: 45
operands: 46
43Operationoperator: 47
operand: 53
44Operationoperator: 49
operand: 54
45Literal
46ExprTuple51, 52
47Literal
48ExprTuple53
49Literal
50ExprTuple54
51Literal
52Literal
53Literal
54Literal