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, Function, Lambda, Omega, Q, Qx, f, fx, g, gy, x, y
from proveit.logic import Bijections, Equals, Forall, Injections
from proveit.statistics import ProbOfAll

# build up the expression from sub-expressions
sub_expr1 = [gy]
expr = Lambda([A, B, Q], Forall(instance_param_or_params = [f, g], instance_expr = 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))), domains = [Injections(A, Omega), Bijections(B, A)]).with_wrapping())

# 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(A, B, Q\right) \mapsto \left[\begin{array}{l}\forall_{f \in \left[A \xrightarrow[]{\text{1-to-1}} \Omega\right], g \in \left[B \xrightarrow[\text{onto}]{\text{1-to-1}} A\right]}~\\
\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]\right)\end{array}\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	51, 53, 49
2	Operation	operator: 3 operand: 5
3	Literal
4	ExprTuple	5
5	Lambda	parameters: 6 body: 7
6	ExprTuple	38, 55
7	Conditional	value: 8 condition: 9
8	Operation	operator: 10 operands: 11
9	Operation	operator: 39 operands: 12
10	Literal
11	ExprTuple	13, 14
12	ExprTuple	15, 16
13	Operation	operator: 18 operand: 22
14	Operation	operator: 18 operand: 23
15	Operation	operator: 47 operands: 20
16	Operation	operator: 47 operands: 21
17	ExprTuple	22
18	Literal
19	ExprTuple	23
20	ExprTuple	38, 24
21	ExprTuple	55, 25
22	Lambda	parameter: 52 body: 26
23	Lambda	parameter: 57 body: 27
24	Operation	operator: 28 operands: 29
25	Operation	operator: 30 operands: 31
26	Conditional	value: 32 condition: 33
27	Conditional	value: 34 condition: 35
28	Literal
29	ExprTuple	51, 36
30	Literal
31	ExprTuple	53, 51
32	Operation	operator: 38 operand: 52
33	Operation	operator: 39 operands: 37
34	Operation	operator: 38 operand: 54
35	Operation	operator: 39 operands: 40
36	Variable
37	ExprTuple	41, 42
38	Variable
39	Literal
40	ExprTuple	43, 44
41	Operation	operator: 47 operands: 45
42	Operation	operator: 49 operand: 52
43	Operation	operator: 47 operands: 48
44	Operation	operator: 49 operand: 54
45	ExprTuple	52, 51
46	ExprTuple	52
47	Literal
48	ExprTuple	57, 53
49	Variable
50	ExprTuple	54
51	Variable
52	Variable
53	Variable
54	Operation	operator: 55 operand: 57
55	Variable
56	ExprTuple	57
57	Variable

Expression of type Lambda¶

from the theory of proveit.statistics¶

Expression of type Lambda ¶

from the theory of proveit.statistics ¶