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

# build up the expression from sub-expressions
sub_expr1 = [gy]
expr = ExprTuple(Lambda([A, B, Q], 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()))

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, Q\right) \mapsto \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]\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	52, 54, 50
3	Operation	operator: 4 operand: 6
4	Literal
5	ExprTuple	6
6	Lambda	parameters: 7 body: 8
7	ExprTuple	39, 56
8	Conditional	value: 9 condition: 10
9	Operation	operator: 11 operands: 12
10	Operation	operator: 40 operands: 13
11	Literal
12	ExprTuple	14, 15
13	ExprTuple	16, 17
14	Operation	operator: 19 operand: 23
15	Operation	operator: 19 operand: 24
16	Operation	operator: 48 operands: 21
17	Operation	operator: 48 operands: 22
18	ExprTuple	23
19	Literal
20	ExprTuple	24
21	ExprTuple	39, 25
22	ExprTuple	56, 26
23	Lambda	parameter: 53 body: 27
24	Lambda	parameter: 58 body: 28
25	Operation	operator: 29 operands: 30
26	Operation	operator: 31 operands: 32
27	Conditional	value: 33 condition: 34
28	Conditional	value: 35 condition: 36
29	Literal
30	ExprTuple	52, 37
31	Literal
32	ExprTuple	54, 52
33	Operation	operator: 39 operand: 53
34	Operation	operator: 40 operands: 38
35	Operation	operator: 39 operand: 55
36	Operation	operator: 40 operands: 41
37	Variable
38	ExprTuple	42, 43
39	Variable
40	Literal
41	ExprTuple	44, 45
42	Operation	operator: 48 operands: 46
43	Operation	operator: 50 operand: 53
44	Operation	operator: 48 operands: 49
45	Operation	operator: 50 operand: 55
46	ExprTuple	53, 52
47	ExprTuple	53
48	Literal
49	ExprTuple	58, 54
50	Variable
51	ExprTuple	55
52	Variable
53	Variable
54	Variable
55	Operation	operator: 56 operand: 58
56	Variable
57	ExprTuple	58
58	Variable