Expression of type Lambda

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, Lambda, Omega, x
from proveit.logic import Forall, InClass, InSet
from proveit.statistics import Prob, SampleSpaces, prob_domain

# build up the expression from sub-expressions
expr = Lambda(Omega, Conditional(Forall(instance_param_or_params = [x], instance_expr = InSet(Prob(x), prob_domain), domain = 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())

\Omega \mapsto \left\{\forall_{x \in \Omega}~\left(\textrm{Pr}\left(x\right) \in \left[0,1\right]\right) \textrm{ if } \Omega \underset{{\scriptscriptstyle c}}{\in} \textrm{SampleSpaces}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 19 body: 2
1	ExprTuple	19
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 9
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	19, 10
9	Lambda	parameter: 24 body: 11
10	Literal
11	Conditional	value: 12 condition: 13
12	Operation	operator: 15 operands: 14
13	Operation	operator: 15 operands: 16
14	ExprTuple	17, 18
15	Literal
16	ExprTuple	24, 19
17	Operation	operator: 20 operand: 24
18	Operation	operator: 22 operands: 23
19	Variable
20	Literal
21	ExprTuple	24
22	Literal
23	ExprTuple	25, 26
24	Variable
25	Literal
26	Literal