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

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(P, Conditional(Forall(instance_param_or_params = [x], instance_expr = Px, domain = Set(a_1_to_n)), And(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(P \mapsto \left\{\forall_{x \in \left\{a_{1}, a_{2}, \ldots, a_{n}\right\}}~P\left(x\right) \textrm{ if } P\left(a_{1}\right) \land  P\left(a_{2}\right) \land  \ldots \land  P\left(a_{n}\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	parameter: 20 body: 3
2	ExprTuple	20
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 10
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10
8	Literal
9	ExprTuple	11
10	Lambda	parameter: 22 body: 12
11	ExprRange	lambda_map: 13 start_index: 28 end_index: 29
12	Conditional	value: 14 condition: 15
13	Lambda	parameter: 33 body: 16
14	Operation	operator: 20 operand: 22
15	Operation	operator: 18 operands: 19
16	Operation	operator: 20 operand: 30
17	ExprTuple	22
18	Literal
19	ExprTuple	22, 23
20	Variable
21	ExprTuple	30
22	Variable
23	Operation	operator: 24 operands: 25
24	Literal
25	ExprTuple	26
26	ExprRange	lambda_map: 27 start_index: 28 end_index: 29
27	Lambda	parameter: 33 body: 30
28	Literal
29	Variable
30	IndexedVar	variable: 31 index: 33
31	Variable
32	ExprTuple	33
33	Variable