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 And, Bijections, Equals, InSet, Injections
from proveit.statistics import ProbOfAll

# build up the expression from sub-expressions
sub_expr1 = [gy]
expr = ExprTuple(Lambda([f, g], Conditional(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))), And(InSet(f, Injections(A, Omega)), InSet(g, Bijections(B, A))))))

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(f, g\right) \mapsto \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] \textrm{ if } f \in \left[A \xrightarrow[]{\text{1-to-1}} \Omega\right] ,  g \in \left[B \xrightarrow[\text{onto}]{\text{1-to-1}} A\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	34, 51
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 35 operands: 8
6	Literal
7	ExprTuple	9, 10
8	ExprTuple	11, 12
9	Operation	operator: 14 operand: 18
10	Operation	operator: 14 operand: 19
11	Operation	operator: 43 operands: 16
12	Operation	operator: 43 operands: 17
13	ExprTuple	18
14	Literal
15	ExprTuple	19
16	ExprTuple	34, 20
17	ExprTuple	51, 21
18	Lambda	parameter: 48 body: 22
19	Lambda	parameter: 53 body: 23
20	Operation	operator: 24 operands: 25
21	Operation	operator: 26 operands: 27
22	Conditional	value: 28 condition: 29
23	Conditional	value: 30 condition: 31
24	Literal
25	ExprTuple	47, 32
26	Literal
27	ExprTuple	49, 47
28	Operation	operator: 34 operand: 48
29	Operation	operator: 35 operands: 33
30	Operation	operator: 34 operand: 50
31	Operation	operator: 35 operands: 36
32	Variable
33	ExprTuple	37, 38
34	Variable
35	Literal
36	ExprTuple	39, 40
37	Operation	operator: 43 operands: 41
38	Operation	operator: 45 operand: 48
39	Operation	operator: 43 operands: 44
40	Operation	operator: 45 operand: 50
41	ExprTuple	48, 47
42	ExprTuple	48
43	Literal
44	ExprTuple	53, 49
45	Variable
46	ExprTuple	50
47	Variable
48	Variable
49	Variable
50	Operation	operator: 51 operand: 53
51	Variable
52	ExprTuple	53
53	Variable