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, Conditional, ExprTuple, Function, Lambda, Omega, Q, Qx, f, fx, g, gy, x, y
from proveit.logic import Bijections, Equals, Forall, InClass, Injections
from proveit.statistics import ProbOfAll, SampleSpaces

# build up the expression from sub-expressions
sub_expr1 = [gy]
expr = ExprTuple(Lambda(Omega, Conditional(Forall(instance_param_or_params = [A, B, Q], instance_expr = Forall(instance_param_or_params = [f, g], instance_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))), domains = [Injections(A, Omega), Bijections(B, A)]).with_wrapping()), InClass(Omega, SampleSpaces))))

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