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 Lambda, Q, Qx, R, Rx, X, fx, x
from proveit.logic import Forall, Implies
from proveit.numbers import LessEq
from proveit.statistics import ProbOfAll

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = Lambda([Q, R], Implies(Forall(instance_param_or_params = sub_expr1, instance_expr = Rx, domain = X, condition = Qx), LessEq(ProbOfAll(instance_param_or_params = sub_expr1, instance_element = fx, domain = X, condition = Qx), ProbOfAll(instance_param_or_params = sub_expr1, instance_element = fx, domain = X, condition = Rx)).with_wrapping_at(2)).with_wrapping_at(2))

expr:

# 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(Q, R\right) \mapsto \left(\begin{array}{c} \begin{array}{l} \left[\forall_{x \in X~|~Q\left(x\right)}~R\left(x\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] \leq  \\ \left[\textrm{Prob}_{x \in X~|~R\left(x\right)}~f\left(x\right)\right] \end{array} \end{array}\right) \end{array} \end{array}\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 1 body: 2
1	ExprTuple	32, 35
2	Operation	operator: 3 operands: 4
3	Literal
4	ExprTuple	5, 6
5	Operation	operator: 7 operand: 11
6	Operation	operator: 9 operands: 10
7	Literal
8	ExprTuple	11
9	Literal
10	ExprTuple	12, 13
11	Lambda	parameter: 38 body: 14
12	Operation	operator: 16 operand: 18
13	Operation	operator: 16 operand: 19
14	Conditional	value: 31 condition: 22
15	ExprTuple	18
16	Literal
17	ExprTuple	19
18	Lambda	parameter: 38 body: 20
19	Lambda	parameter: 38 body: 21
20	Conditional	value: 23 condition: 22
21	Conditional	value: 23 condition: 24
22	Operation	operator: 27 operands: 25
23	Operation	operator: 26 operand: 38
24	Operation	operator: 27 operands: 28
25	ExprTuple	30, 29
26	Variable
27	Literal
28	ExprTuple	30, 31
29	Operation	operator: 32 operand: 38
30	Operation	operator: 33 operands: 34
31	Operation	operator: 35 operand: 38
32	Variable
33	Literal
34	ExprTuple	38, 37
35	Variable
36	ExprTuple	38
37	Variable
38	Variable