Expression of type Conditional ¶

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, 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 = 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))

# 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\{\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..

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
0	Conditional	value: 1 condition: 2
1	Operation	operator: 21 operand: 5
2	Operation	operator: 23 operands: 4
3	ExprTuple	5
4	ExprTuple	37, 28
5	Lambda	parameters: 34 body: 6
6	Operation	operator: 21 operand: 8
7	ExprTuple	8
8	Lambda	parameters: 9 body: 10
9	ExprTuple	51, 52
10	Conditional	value: 11 condition: 12
11	Operation	operator: 13 operands: 14
12	Operation	operator: 15 operands: 16
13	Literal
14	ExprTuple	17, 18
15	Literal
16	ExprTuple	19, 20
17	Operation	operator: 21 operand: 27
18	Operation	operator: 23 operands: 24
19	Operation	operator: 41 operands: 25
20	Operation	operator: 41 operands: 26
21	Literal
22	ExprTuple	27
23	Literal
24	ExprTuple	38, 28
25	ExprTuple	51, 29
26	ExprTuple	52, 30
27	Lambda	parameter: 54 body: 31
28	Literal
29	Operation	operator: 33 operands: 32
30	Operation	operator: 33 operands: 34
31	Conditional	value: 35 condition: 36
32	ExprTuple	45, 37
33	Literal
34	ExprTuple	45, 38
35	Operation	operator: 39 operands: 40
36	Operation	operator: 41 operands: 42
37	Variable
38	Variable
39	Literal
40	ExprTuple	43, 44
41	Literal
42	ExprTuple	54, 45
43	Operation	operator: 47 operand: 49
44	Operation	operator: 47 operand: 50
45	Variable
46	ExprTuple	49
47	Literal
48	ExprTuple	50
49	Operation	operator: 51 operand: 54
50	Operation	operator: 52 operand: 54
51	Variable
52	Variable
53	ExprTuple	54
54	Variable

Expression of type Conditional¶

from the theory of proveit.statistics¶

Expression of type Conditional ¶

from the theory of proveit.statistics ¶