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Expression of type Conditional

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 A, B, Conditional, Omega
from proveit.logic import And, SubsetEq
from proveit.numbers import LessEq
from proveit.statistics import Prob
In [2]:
# build up the expression from sub-expressions
expr = Conditional(LessEq(Prob(A), Prob(B)), And(SubsetEq(A, B), SubsetEq(B, Omega)).with_total_ordering_style())
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())
\left\{\textrm{Pr}\left(A\right) \leq \textrm{Pr}\left(B\right) \textrm{ if } A \subseteq B ,  B \subseteq \Omega\right..
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
condition_delimiter'comma' or 'and'commacomma('with_comma_delimiter', 'with_conjunction_delimiter')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 3
operands: 4
2Operationoperator: 5
operands: 6
3Literal
4ExprTuple7, 8
5Literal
6ExprTuple9, 10
7Operationoperator: 12
operand: 17
8Operationoperator: 12
operand: 18
9Operationoperator: 15
operands: 14
10Operationoperator: 15
operands: 16
11ExprTuple17
12Literal
13ExprTuple18
14ExprTuple17, 18
15Literal
16ExprTuple18, 19
17Variable
18Variable
19Variable