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 Bijections, Equals, Forall, Implies, InClass
from proveit.statistics import Prob, SampleSpaces

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(Omega, Conditional(Forall(instance_param_or_params = [X, Y], instance_expr = 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)])), 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_{X, Y}~\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] \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: 40 body: 3
2	ExprTuple	40
3	Conditional	value: 4 condition: 5
4	Operation	operator: 24 operand: 8
5	Operation	operator: 26 operands: 7
6	ExprTuple	8
7	ExprTuple	40, 31
8	Lambda	parameters: 37 body: 9
9	Operation	operator: 24 operand: 11
10	ExprTuple	11
11	Lambda	parameters: 12 body: 13
12	ExprTuple	54, 55
13	Conditional	value: 14 condition: 15
14	Operation	operator: 16 operands: 17
15	Operation	operator: 18 operands: 19
16	Literal
17	ExprTuple	20, 21
18	Literal
19	ExprTuple	22, 23
20	Operation	operator: 24 operand: 30
21	Operation	operator: 26 operands: 27
22	Operation	operator: 44 operands: 28
23	Operation	operator: 44 operands: 29
24	Literal
25	ExprTuple	30
26	Literal
27	ExprTuple	41, 31
28	ExprTuple	54, 32
29	ExprTuple	55, 33
30	Lambda	parameter: 57 body: 34
31	Literal
32	Operation	operator: 36 operands: 35
33	Operation	operator: 36 operands: 37
34	Conditional	value: 38 condition: 39
35	ExprTuple	48, 40
36	Literal
37	ExprTuple	48, 41
38	Operation	operator: 42 operands: 43
39	Operation	operator: 44 operands: 45
40	Variable
41	Variable
42	Literal
43	ExprTuple	46, 47
44	Literal
45	ExprTuple	57, 48
46	Operation	operator: 50 operand: 52
47	Operation	operator: 50 operand: 53
48	Variable
49	ExprTuple	52
50	Literal
51	ExprTuple	53
52	Operation	operator: 54 operand: 57
53	Operation	operator: 55 operand: 57
54	Variable
55	Variable
56	ExprTuple	57
57	Variable