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, Q, Qx, X, f, fx, x
from proveit.logic import Equals, Forall, InSet, Injections
from proveit.numbers import Sum
from proveit.statistics import Prob, ProbOfAll

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = Conditional(Forall(instance_param_or_params = [Q], instance_expr = Equals(ProbOfAll(instance_param_or_params = sub_expr1, instance_element = fx, domain = X, condition = Qx), Sum(index_or_indices = sub_expr1, summand = Prob(fx), domain = X, condition = Qx)).with_wrapping_at(2)), InSet(f, Injections(X, Omega)))

# 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_{Q}~\left(\begin{array}{c} \begin{array}{l} \left[\textrm{Prob}_{x \in X~|~Q\left(x\right)}~f\left(x\right)\right] =  \\ \left[\sum_{x \in X~|~Q\left(x\right)}~\textrm{Pr}\left(f\left(x\right)\right)\right] \end{array} \end{array}\right) \textrm{ if } f \in \left[X \xrightarrow[]{\text{1-to-1}} \Omega\right]\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: 3 operand: 6
2	Operation	operator: 35 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	34, 7
6	Lambda	parameter: 37 body: 9
7	Operation	operator: 10 operands: 11
8	ExprTuple	37
9	Operation	operator: 12 operands: 13
10	Literal
11	ExprTuple	39, 14
12	Literal
13	ExprTuple	15, 16
14	Variable
15	Operation	operator: 17 operand: 21
16	Operation	operator: 19 operand: 22
17	Literal
18	ExprTuple	21
19	Literal
20	ExprTuple	22
21	Lambda	parameter: 40 body: 23
22	Lambda	parameter: 40 body: 24
23	Conditional	value: 31 condition: 26
24	Conditional	value: 25 condition: 26
25	Operation	operator: 27 operand: 31
26	Operation	operator: 29 operands: 30
27	Literal
28	ExprTuple	31
29	Literal
30	ExprTuple	32, 33
31	Operation	operator: 34 operand: 40
32	Operation	operator: 35 operands: 36
33	Operation	operator: 37 operand: 40
34	Variable
35	Literal
36	ExprTuple	40, 39
37	Variable
38	ExprTuple	40
39	Variable
40	Variable

Expression of type Conditional¶

from the theory of proveit.statistics¶

Expression of type Conditional ¶

from the theory of proveit.statistics ¶