Expression of type Add

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 A, B, Qx, fx, x
from proveit.numbers import Add
from proveit.statistics import ProbOfAll

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = Add(ProbOfAll(instance_param_or_params = sub_expr1, instance_element = fx, domain = A, condition = Qx), ProbOfAll(instance_param_or_params = sub_expr1, instance_element = fx, domain = B, condition = Qx))

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[\textrm{Prob}_{x \in A~|~Q\left(x\right)}~f\left(x\right)\right] + \left[\textrm{Prob}_{x \in B~|~Q\left(x\right)}~f\left(x\right)\right]

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 6 operand: 8
4	Operation	operator: 6 operand: 9
5	ExprTuple	8
6	Literal
7	ExprTuple	9
8	Lambda	parameter: 29 body: 10
9	Lambda	parameter: 29 body: 11
10	Conditional	value: 13 condition: 12
11	Conditional	value: 13 condition: 14
12	Operation	operator: 17 operands: 15
13	Operation	operator: 16 operand: 29
14	Operation	operator: 17 operands: 18
15	ExprTuple	19, 21
16	Variable
17	Literal
18	ExprTuple	20, 21
19	Operation	operator: 23 operands: 22
20	Operation	operator: 23 operands: 24
21	Operation	operator: 25 operand: 29
22	ExprTuple	29, 27
23	Literal
24	ExprTuple	29, 28
25	Variable
26	ExprTuple	29
27	Variable
28	Variable
29	Variable