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, Q, Qx, X, f, fx, x
from proveit.logic import And, Disjoint, Equals, Forall, Injections, SubsetEq, Union
from proveit.numbers import Add
from proveit.statistics import ProbOfAll

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = ExprTuple(Lambda([A, B, C, X, Q], Conditional(Forall(instance_param_or_params = [f], instance_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))), domain = Injections(X, Omega)), And(SubsetEq(C, X), Equals(C, Union(A, B)), Disjoint(A, B)))))

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(\left(A, B, C, X, Q\right) \mapsto \left\{\forall_{f \in \left[X \xrightarrow[]{\text{1-to-1}} \Omega\right]}~\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)\right) \textrm{ if } C \subseteq X ,  C = \left(A \cup B\right) ,  \textrm{disjoint}\left(A, B\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	parameters: 2 body: 3
2	ExprTuple	68, 69, 59, 38, 66
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 57 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	10, 11, 12
9	Lambda	parameter: 56 body: 14
10	Operation	operator: 15 operands: 16
11	Operation	operator: 22 operands: 17
12	Operation	operator: 18 operands: 26
13	ExprTuple	56
14	Conditional	value: 19 condition: 20
15	Literal
16	ExprTuple	59, 38
17	ExprTuple	59, 21
18	Literal
19	Operation	operator: 22 operands: 23
20	Operation	operator: 64 operands: 24
21	Operation	operator: 25 operands: 26
22	Literal
23	ExprTuple	27, 28
24	ExprTuple	56, 29
25	Literal
26	ExprTuple	68, 69
27	Operation	operator: 42 operand: 35
28	Operation	operator: 31 operands: 32
29	Operation	operator: 33 operands: 34
30	ExprTuple	35
31	Literal
32	ExprTuple	36, 37
33	Literal
34	ExprTuple	38, 39
35	Lambda	parameter: 70 body: 40
36	Operation	operator: 42 operand: 45
37	Operation	operator: 42 operand: 46
38	Variable
39	Variable
40	Conditional	value: 52 condition: 44
41	ExprTuple	45
42	Literal
43	ExprTuple	46
44	Operation	operator: 57 operands: 47
45	Lambda	parameter: 70 body: 48
46	Lambda	parameter: 70 body: 49
47	ExprTuple	50, 62
48	Conditional	value: 52 condition: 51
49	Conditional	value: 52 condition: 53
50	Operation	operator: 64 operands: 54
51	Operation	operator: 57 operands: 55
52	Operation	operator: 56 operand: 70
53	Operation	operator: 57 operands: 58
54	ExprTuple	70, 59
55	ExprTuple	60, 62
56	Variable
57	Literal
58	ExprTuple	61, 62
59	Variable
60	Operation	operator: 64 operands: 63
61	Operation	operator: 64 operands: 65
62	Operation	operator: 66 operand: 70
63	ExprTuple	70, 68
64	Literal
65	ExprTuple	70, 69
66	Variable
67	ExprTuple	70
68	Variable
69	Variable
70	Variable