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, Function, Q, Qx, f, fx, gy, x, y
from proveit.logic import Equals
from proveit.statistics import ProbOfAll

# build up the expression from sub-expressions
sub_expr1 = [gy]
expr = Equals(ProbOfAll(instance_param_or_params = [x], instance_element = fx, domain = A, condition = Qx), ProbOfAll(instance_param_or_params = [y], instance_element = Function(f, sub_expr1), domain = B, condition = Function(Q, sub_expr1)))

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}_{y \in B~|~Q\left(g\left(y\right)\right)}~f\left(g\left(y\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: 6 operand: 8
4	Operation	operator: 6 operand: 9
5	ExprTuple	8
6	Literal
7	ExprTuple	9
8	Lambda	parameter: 31 body: 10
9	Lambda	parameter: 36 body: 11
10	Conditional	value: 12 condition: 13
11	Conditional	value: 14 condition: 15
12	Operation	operator: 17 operand: 31
13	Operation	operator: 18 operands: 16
14	Operation	operator: 17 operand: 33
15	Operation	operator: 18 operands: 19
16	ExprTuple	20, 21
17	Variable
18	Literal
19	ExprTuple	22, 23
20	Operation	operator: 26 operands: 24
21	Operation	operator: 28 operand: 31
22	Operation	operator: 26 operands: 27
23	Operation	operator: 28 operand: 33
24	ExprTuple	31, 30
25	ExprTuple	31
26	Literal
27	ExprTuple	36, 32
28	Variable
29	ExprTuple	33
30	Variable
31	Variable
32	Variable
33	Operation	operator: 34 operand: 36
34	Variable
35	ExprTuple	36
36	Variable