Expression of type Lambda ¶

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, Lambda, Omega, Q, Qx, R, Rx, Ry, X, f, fx, fy, x, y
from proveit.logic import Bijections, Equals, Forall, Implies, InSet, Not
from proveit.numbers import one, subtract
from proveit.statistics import ProbOfAll

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = Lambda(f, Conditional(Forall(instance_param_or_params = [Q, R], instance_expr = Implies(Forall(instance_param_or_params = sub_expr1, instance_expr = Equals(Qx, Not(Rx)), domain = X), Equals(ProbOfAll(instance_param_or_params = sub_expr1, instance_element = fx, domain = X, condition = Qx), subtract(one, ProbOfAll(instance_param_or_params = [y], instance_element = fy, domain = X, condition = Ry))).with_wrapping_at(2)).with_wrapping_at(2)), InSet(f, Bijections(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())

f \mapsto \left\{\forall_{Q, R}~\left(\begin{array}{c} \begin{array}{l} \left[\forall_{x \in X}~\left(Q\left(x\right) = (\lnot R\left(x\right))\right)\right] \Rightarrow  \\ \left(\begin{array}{c} \begin{array}{l} \left[\textrm{Prob}_{x \in X~|~Q\left(x\right)}~f\left(x\right)\right] =  \\ \left(1 - \left[\textrm{Prob}_{y \in X~|~R\left(y\right)}~f\left(y\right)\right]\right) \end{array} \end{array}\right) \end{array} \end{array}\right) \textrm{ if } f \in \left[X \xrightarrow[\text{onto}]{\text{1-to-1}} \Omega\right]\right..

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
0	Lambda	parameter: 57 body: 2
1	ExprTuple	57
2	Conditional	value: 3 condition: 4
3	Operation	operator: 18 operand: 7
4	Operation	operator: 62 operands: 6
5	ExprTuple	7
6	ExprTuple	57, 8
7	Lambda	parameters: 9 body: 10
8	Operation	operator: 11 operands: 12
9	ExprTuple	51, 64
10	Operation	operator: 13 operands: 14
11	Literal
12	ExprTuple	66, 15
13	Literal
14	ExprTuple	16, 17
15	Variable
16	Operation	operator: 18 operand: 21
17	Operation	operator: 32 operands: 20
18	Literal
19	ExprTuple	21
20	ExprTuple	22, 23
21	Lambda	parameter: 54 body: 24
22	Operation	operator: 44 operand: 29
23	Operation	operator: 26 operands: 27
24	Conditional	value: 28 condition: 47
25	ExprTuple	29
26	Literal
27	ExprTuple	30, 31
28	Operation	operator: 32 operands: 33
29	Lambda	parameter: 54 body: 34
30	Literal
31	Operation	operator: 35 operand: 40
32	Literal
33	ExprTuple	48, 37
34	Conditional	value: 38 condition: 39
35	Literal
36	ExprTuple	40
37	Operation	operator: 41 operand: 46
38	Operation	operator: 57 operand: 54
39	Operation	operator: 58 operands: 43
40	Operation	operator: 44 operand: 49
41	Literal
42	ExprTuple	46
43	ExprTuple	47, 48
44	Literal
45	ExprTuple	49
46	Operation	operator: 64 operand: 54
47	Operation	operator: 62 operands: 50
48	Operation	operator: 51 operand: 54
49	Lambda	parameter: 67 body: 53
50	ExprTuple	54, 66
51	Variable
52	ExprTuple	54
53	Conditional	value: 55 condition: 56
54	Variable
55	Operation	operator: 57 operand: 67
56	Operation	operator: 58 operands: 59
57	Variable
58	Literal
59	ExprTuple	60, 61
60	Operation	operator: 62 operands: 63
61	Operation	operator: 64 operand: 67
62	Literal
63	ExprTuple	67, 66
64	Variable
65	ExprTuple	67
66	Variable
67	Variable

Expression of type Lambda¶

from the theory of proveit.statistics¶

Expression of type Lambda ¶

from the theory of proveit.statistics ¶