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, X, fx, gx, x
from proveit.logic import Equals, InSet
from proveit.statistics import Prob

# build up the expression from sub-expressions
expr = Lambda(x, Conditional(Equals(Prob(fx), Prob(gx)), InSet(x, X)))

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())

x \mapsto \left\{\textrm{Pr}\left(f\left(x\right)\right) = \textrm{Pr}\left(g\left(x\right)\right) \textrm{ if } x \in X\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: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	19, 10
8	Operation	operator: 12 operand: 14
9	Operation	operator: 12 operand: 15
10	Variable
11	ExprTuple	14
12	Literal
13	ExprTuple	15
14	Operation	operator: 16 operand: 19
15	Operation	operator: 17 operand: 19
16	Variable
17	Variable
18	ExprTuple	19
19	Variable