Expression of type ExprTuple

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 ExprTuple, Lambda, P, Px, x
from proveit.core_expr_types import Pk_a1_to_an, a_1_to_n
from proveit.logic import And, Equals, Forall, Set

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

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

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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