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 A, B, Conditional, Function, Omega, Q, Qx, f, fx, g, gy, x, y
from proveit.logic import And, Bijections, Equals, InSet, Injections
from proveit.statistics import ProbOfAll

# build up the expression from sub-expressions
sub_expr1 = [gy]
expr = Conditional(Equals(ProbOfAll(instance_param_or_params = [x], instance_element = fx, domain = A, condition = Qx), ProbOfAll(instance_param_or_params = [y], instance_element = Function(f, sub_expr1), domain = B, condition = Function(Q, sub_expr1))), And(InSet(f, Injections(A, Omega)), InSet(g, Bijections(B, A))))

# 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[\textrm{Prob}_{x \in A~|~Q\left(x\right)}~f\left(x\right)\right] = \left[\textrm{Prob}_{y \in B~|~Q\left(g\left(y\right)\right)}~f\left(g\left(y\right)\right)\right] \textrm{ if } f \in \left[A \xrightarrow[]{\text{1-to-1}} \Omega\right] ,  g \in \left[B \xrightarrow[\text{onto}]{\text{1-to-1}} A\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 operands: 4
2	Operation	operator: 32 operands: 5
3	Literal
4	ExprTuple	6, 7
5	ExprTuple	8, 9
6	Operation	operator: 11 operand: 15
7	Operation	operator: 11 operand: 16
8	Operation	operator: 40 operands: 13
9	Operation	operator: 40 operands: 14
10	ExprTuple	15
11	Literal
12	ExprTuple	16
13	ExprTuple	31, 17
14	ExprTuple	48, 18
15	Lambda	parameter: 45 body: 19
16	Lambda	parameter: 50 body: 20
17	Operation	operator: 21 operands: 22
18	Operation	operator: 23 operands: 24
19	Conditional	value: 25 condition: 26
20	Conditional	value: 27 condition: 28
21	Literal
22	ExprTuple	44, 29
23	Literal
24	ExprTuple	46, 44
25	Operation	operator: 31 operand: 45
26	Operation	operator: 32 operands: 30
27	Operation	operator: 31 operand: 47
28	Operation	operator: 32 operands: 33
29	Variable
30	ExprTuple	34, 35
31	Variable
32	Literal
33	ExprTuple	36, 37
34	Operation	operator: 40 operands: 38
35	Operation	operator: 42 operand: 45
36	Operation	operator: 40 operands: 41
37	Operation	operator: 42 operand: 47
38	ExprTuple	45, 44
39	ExprTuple	45
40	Literal
41	ExprTuple	50, 46
42	Variable
43	ExprTuple	47
44	Variable
45	Variable
46	Variable
47	Operation	operator: 48 operand: 50
48	Variable
49	ExprTuple	50
50	Variable

Expression of type Conditional¶

from the theory of proveit.statistics¶

Expression of type Conditional ¶

from the theory of proveit.statistics ¶