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

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([f, g], Conditional(Implies(Forall(instance_param_or_params = [x], instance_expr = Equals(Prob(fx), Prob(gx)), domain = X), InClass(Y, SampleSpaces)).with_wrapping_at(1), And(InSet(f, Bijections(X, Omega)), InSet(g, 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(f, g\right) \mapsto \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} \textrm{ if } 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]\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	44, 45
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	12, 13
10	Operation	operator: 14 operand: 20
11	Operation	operator: 16 operands: 17
12	Operation	operator: 34 operands: 18
13	Operation	operator: 34 operands: 19
14	Literal
15	ExprTuple	20
16	Literal
17	ExprTuple	31, 21
18	ExprTuple	44, 22
19	ExprTuple	45, 23
20	Lambda	parameter: 47 body: 24
21	Literal
22	Operation	operator: 26 operands: 25
23	Operation	operator: 26 operands: 27
24	Conditional	value: 28 condition: 29
25	ExprTuple	38, 30
26	Literal
27	ExprTuple	38, 31
28	Operation	operator: 32 operands: 33
29	Operation	operator: 34 operands: 35
30	Variable
31	Variable
32	Literal
33	ExprTuple	36, 37
34	Literal
35	ExprTuple	47, 38
36	Operation	operator: 40 operand: 42
37	Operation	operator: 40 operand: 43
38	Variable
39	ExprTuple	42
40	Literal
41	ExprTuple	43
42	Operation	operator: 44 operand: 47
43	Operation	operator: 45 operand: 47
44	Variable
45	Variable
46	ExprTuple	47
47	Variable