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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, subtract, two
from proveit.physics.quantum.QPE import _pos_domain
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [l], instance_expr = InSet(frac(one, Exp(subtract(l, one), 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 - 1\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: 32
body: 5
4ExprTuple32
5Conditionalvalue: 6
condition: 7
6Operationoperator: 9
operands: 8
7Operationoperator: 9
operands: 10
8ExprTuple11, 12
9Literal
10ExprTuple32, 13
11Operationoperator: 14
operands: 15
12Literal
13Operationoperator: 16
operands: 17
14Literal
15ExprTuple37, 18
16Literal
17ExprTuple19, 20
18Operationoperator: 23
operands: 21
19Operationoperator: 30
operands: 22
20Operationoperator: 23
operands: 24
21ExprTuple25, 27
22ExprTuple26, 37
23Literal
24ExprTuple27, 28
25Operationoperator: 30
operands: 29
26Variable
27Literal
28Operationoperator: 30
operands: 31
29ExprTuple32, 34
30Literal
31ExprTuple33, 34
32Variable
33Literal
34Operationoperator: 35
operand: 37
35Literal
36ExprTuple37
37Literal