Expression of type ExprTuple

from the theory of proveit.statistics

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 Conditional, ExprTuple, Lambda, Omega, S
from proveit.logic import Difference, Equals, SubsetEq
from proveit.numbers import one, subtract
from proveit.statistics import Prob

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(S, Conditional(Equals(Prob(Difference(Omega, S)), subtract(one, Prob(S))), SubsetEq(S, Omega))))

expr:

# 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

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(S \mapsto \left\{\textrm{Pr}\left(\Omega - S\right) = \left(1 - \textrm{Pr}\left(S\right)\right) \textrm{ if } S \subseteq \Omega\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 25 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	25, 21
9	Operation	operator: 23 operand: 14
10	Operation	operator: 12 operands: 13
11	ExprTuple	14
12	Literal
13	ExprTuple	15, 16
14	Operation	operator: 17 operands: 18
15	Literal
16	Operation	operator: 19 operand: 22
17	Literal
18	ExprTuple	21, 25
19	Literal
20	ExprTuple	22
21	Variable
22	Operation	operator: 23 operand: 25
23	Literal
24	ExprTuple	25
25	Variable