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Expression of type Equals

from the theory of proveit.statistics

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 Qx, X, fx, x
from proveit.logic import Equals
from proveit.numbers import Sum
from proveit.statistics import Prob, ProbOfAll
In [2]:
# build up the expression from sub-expressions
sub_expr1 = [x]
expr = Equals(ProbOfAll(instance_param_or_params = sub_expr1, instance_element = fx, domain = X, condition = Qx), Sum(index_or_indices = sub_expr1, summand = Prob(fx), domain = X, condition = Qx)).with_wrapping_at(2)
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())
\begin{array}{c} \begin{array}{l} \left[\textrm{Prob}_{x \in X~|~Q\left(x\right)}~f\left(x\right)\right] =  \\ \left[\sum_{x \in X~|~Q\left(x\right)}~\textrm{Pr}\left(f\left(x\right)\right)\right] \end{array} \end{array}
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.()(2)('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
directionDirection of the relation (normal or reversed)normalnormal('with_direction_reversed', 'is_reversed')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4
3Operationoperator: 5
operand: 9
4Operationoperator: 7
operand: 10
5Literal
6ExprTuple9
7Literal
8ExprTuple10
9Lambdaparameter: 28
body: 11
10Lambdaparameter: 28
body: 12
11Conditionalvalue: 19
condition: 14
12Conditionalvalue: 13
condition: 14
13Operationoperator: 15
operand: 19
14Operationoperator: 17
operands: 18
15Literal
16ExprTuple19
17Literal
18ExprTuple20, 21
19Operationoperator: 22
operand: 28
20Operationoperator: 23
operands: 24
21Operationoperator: 25
operand: 28
22Variable
23Literal
24ExprTuple28, 27
25Variable
26ExprTuple28
27Variable
28Variable