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 A, B, Conditional, Function, Lambda, 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 = Lambda([f, g], 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(f, g\right) \mapsto \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	Lambda	parameters: 1 body: 2
1	ExprTuple	33, 50
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 34 operands: 7
5	Literal
6	ExprTuple	8, 9
7	ExprTuple	10, 11
8	Operation	operator: 13 operand: 17
9	Operation	operator: 13 operand: 18
10	Operation	operator: 42 operands: 15
11	Operation	operator: 42 operands: 16
12	ExprTuple	17
13	Literal
14	ExprTuple	18
15	ExprTuple	33, 19
16	ExprTuple	50, 20
17	Lambda	parameter: 47 body: 21
18	Lambda	parameter: 52 body: 22
19	Operation	operator: 23 operands: 24
20	Operation	operator: 25 operands: 26
21	Conditional	value: 27 condition: 28
22	Conditional	value: 29 condition: 30
23	Literal
24	ExprTuple	46, 31
25	Literal
26	ExprTuple	48, 46
27	Operation	operator: 33 operand: 47
28	Operation	operator: 34 operands: 32
29	Operation	operator: 33 operand: 49
30	Operation	operator: 34 operands: 35
31	Variable
32	ExprTuple	36, 37
33	Variable
34	Literal
35	ExprTuple	38, 39
36	Operation	operator: 42 operands: 40
37	Operation	operator: 44 operand: 47
38	Operation	operator: 42 operands: 43
39	Operation	operator: 44 operand: 49
40	ExprTuple	47, 46
41	ExprTuple	47
42	Literal
43	ExprTuple	52, 48
44	Variable
45	ExprTuple	49
46	Variable
47	Variable
48	Variable
49	Operation	operator: 50 operand: 52
50	Variable
51	ExprTuple	52
52	Variable

Expression of type Lambda¶

from the theory of proveit.statistics¶

Expression of type Lambda ¶

from the theory of proveit.statistics ¶