Expression of type ExprTuple

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, Conditional, ExprTuple, Lambda, Omega, Qx, X, f, fx, x
from proveit.logic import Equals, InSet, Injections
from proveit.numbers import Add
from proveit.statistics import ProbOfAll

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = ExprTuple(Lambda(f, Conditional(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))), InSet(f, Injections(X, Omega)))))

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(f \mapsto \left\{\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) \textrm{ if } f \in \left[X \xrightarrow[]{\text{1-to-1}} \Omega\right]\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 38 body: 3
2	ExprTuple	38
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 46 operands: 8
6	Literal
7	ExprTuple	9, 10
8	ExprTuple	38, 11
9	Operation	operator: 24 operand: 17
10	Operation	operator: 13 operands: 14
11	Operation	operator: 15 operands: 16
12	ExprTuple	17
13	Literal
14	ExprTuple	18, 19
15	Literal
16	ExprTuple	20, 21
17	Lambda	parameter: 52 body: 22
18	Operation	operator: 24 operand: 27
19	Operation	operator: 24 operand: 28
20	Variable
21	Variable
22	Conditional	value: 34 condition: 26
23	ExprTuple	27
24	Literal
25	ExprTuple	28
26	Operation	operator: 39 operands: 29
27	Lambda	parameter: 52 body: 30
28	Lambda	parameter: 52 body: 31
29	ExprTuple	32, 44
30	Conditional	value: 34 condition: 33
31	Conditional	value: 34 condition: 35
32	Operation	operator: 46 operands: 36
33	Operation	operator: 39 operands: 37
34	Operation	operator: 38 operand: 52
35	Operation	operator: 39 operands: 40
36	ExprTuple	52, 41
37	ExprTuple	42, 44
38	Variable
39	Literal
40	ExprTuple	43, 44
41	Variable
42	Operation	operator: 46 operands: 45
43	Operation	operator: 46 operands: 47
44	Operation	operator: 48 operand: 52
45	ExprTuple	52, 50
46	Literal
47	ExprTuple	52, 51
48	Variable
49	ExprTuple	52
50	Variable
51	Variable
52	Variable