Expression of type Lambda

from the theory of proveit.logic.sets.enumeration

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, P, Px, x
from proveit.core_expr_types import Pk_a1_to_an, a_1_to_n
from proveit.logic import Forall, Set

# build up the expression from sub-expressions
expr = Lambda([a_1_to_n], Forall(instance_param_or_params = [P], instance_expr = Forall(instance_param_or_params = [x], instance_expr = Px, domain = Set(a_1_to_n)), condition = Pk_a1_to_an))

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(a_{1}, a_{2}, \ldots, a_{n}\right) \mapsto \left[\forall_{P~|~P\left(a_{1}\right), P\left(a_{2}\right), \ldots, P\left(a_{n}\right)}~\left[\forall_{x \in \left\{a_{1}, a_{2}, \ldots, a_{n}\right\}}~P\left(x\right)\right]\right]

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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