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, Forall, InClass, SubsetEq
from proveit.numbers import one, subtract
from proveit.statistics import Prob, SampleSpaces

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(Omega, Conditional(Forall(instance_param_or_params = [S], instance_expr = Equals(Prob(Difference(Omega, S)), subtract(one, Prob(S))), condition = SubsetEq(S, Omega)), InClass(Omega, SampleSpaces))))

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(\Omega \mapsto \left\{\forall_{S~|~S \subseteq \Omega}~\left(\textrm{Pr}\left(\Omega - S\right) = \left(1 - \textrm{Pr}\left(S\right)\right)\right) \textrm{ if } \Omega \underset{{\scriptscriptstyle c}}{\in} \textrm{SampleSpaces}\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: 31 body: 3
2	ExprTuple	31
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 10
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10
8	Literal
9	ExprTuple	31, 11
10	Lambda	parameter: 35 body: 12
11	Literal
12	Conditional	value: 13 condition: 14
13	Operation	operator: 15 operands: 16
14	Operation	operator: 17 operands: 18
15	Literal
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	35, 31
19	Operation	operator: 33 operand: 24
20	Operation	operator: 22 operands: 23
21	ExprTuple	24
22	Literal
23	ExprTuple	25, 26
24	Operation	operator: 27 operands: 28
25	Literal
26	Operation	operator: 29 operand: 32
27	Literal
28	ExprTuple	31, 35
29	Literal
30	ExprTuple	32
31	Variable
32	Operation	operator: 33 operand: 35
33	Literal
34	ExprTuple	35
35	Variable