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 ExprTuple, Lambda, Omega, X, Y, f, fx, g, gx, x
from proveit.logic import Bijections, Equals, Forall, Implies, InClass
from proveit.statistics import Prob, SampleSpaces

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([X, Y], Forall(instance_param_or_params = [f, g], instance_expr = Implies(Forall(instance_param_or_params = [x], instance_expr = Equals(Prob(fx), Prob(gx)), domain = X), InClass(Y, SampleSpaces)).with_wrapping_at(1), domains = [Bijections(X, Omega), Bijections(X, Y)])))

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(X, Y\right) \mapsto \left[\forall_{f \in \left[X \xrightarrow[\text{onto}]{\text{1-to-1}} \Omega\right], g \in \left[X \xrightarrow[\text{onto}]{\text{1-to-1}} Y\right]}~\left(\begin{array}{c} \begin{array}{l} \left[\forall_{x \in X}~\left(\textrm{Pr}\left(f\left(x\right)\right) = \textrm{Pr}\left(g\left(x\right)\right)\right)\right] \\  \Rightarrow \left(Y \underset{{\scriptscriptstyle c}}{\in} \textrm{SampleSpaces}\right) \end{array} \end{array}\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: 30 body: 2
2	Operation	operator: 17 operand: 4
3	ExprTuple	4
4	Lambda	parameters: 5 body: 6
5	ExprTuple	47, 48
6	Conditional	value: 7 condition: 8
7	Operation	operator: 9 operands: 10
8	Operation	operator: 11 operands: 12
9	Literal
10	ExprTuple	13, 14
11	Literal
12	ExprTuple	15, 16
13	Operation	operator: 17 operand: 23
14	Operation	operator: 19 operands: 20
15	Operation	operator: 37 operands: 21
16	Operation	operator: 37 operands: 22
17	Literal
18	ExprTuple	23
19	Literal
20	ExprTuple	34, 24
21	ExprTuple	47, 25
22	ExprTuple	48, 26
23	Lambda	parameter: 50 body: 27
24	Literal
25	Operation	operator: 29 operands: 28
26	Operation	operator: 29 operands: 30
27	Conditional	value: 31 condition: 32
28	ExprTuple	41, 33
29	Literal
30	ExprTuple	41, 34
31	Operation	operator: 35 operands: 36
32	Operation	operator: 37 operands: 38
33	Variable
34	Variable
35	Literal
36	ExprTuple	39, 40
37	Literal
38	ExprTuple	50, 41
39	Operation	operator: 43 operand: 45
40	Operation	operator: 43 operand: 46
41	Variable
42	ExprTuple	45
43	Literal
44	ExprTuple	46
45	Operation	operator: 47 operand: 50
46	Operation	operator: 48 operand: 50
47	Variable
48	Variable
49	ExprTuple	50
50	Variable