Expression of type Equals

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, C, Qx, fx, x
from proveit.logic import Equals
from proveit.numbers import Add
from proveit.statistics import ProbOfAll

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = Equals(ProbOfAll(instance_param_or_params = sub_expr1, instance_element = fx, domain = C, condition = Qx), 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 C~|~Q\left(x\right)}~f\left(x\right)\right] = \left(\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]\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',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# 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: 13 operand: 8
4	Operation	operator: 6 operands: 7
5	ExprTuple	8
6	Literal
7	ExprTuple	9, 10
8	Lambda	parameter: 41 body: 11
9	Operation	operator: 13 operand: 16
10	Operation	operator: 13 operand: 17
11	Conditional	value: 23 condition: 15
12	ExprTuple	16
13	Literal
14	ExprTuple	17
15	Operation	operator: 28 operands: 18
16	Lambda	parameter: 41 body: 19
17	Lambda	parameter: 41 body: 20
18	ExprTuple	21, 33
19	Conditional	value: 23 condition: 22
20	Conditional	value: 23 condition: 24
21	Operation	operator: 35 operands: 25
22	Operation	operator: 28 operands: 26
23	Operation	operator: 27 operand: 41
24	Operation	operator: 28 operands: 29
25	ExprTuple	41, 30
26	ExprTuple	31, 33
27	Variable
28	Literal
29	ExprTuple	32, 33
30	Variable
31	Operation	operator: 35 operands: 34
32	Operation	operator: 35 operands: 36
33	Operation	operator: 37 operand: 41
34	ExprTuple	41, 39
35	Literal
36	ExprTuple	41, 40
37	Variable
38	ExprTuple	41
39	Variable
40	Variable
41	Variable