Expression of type ExprTuple

from the theory of proveit.logic.sets.cartesian_products

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, x
from proveit.core_expr_types import A_1_to_m, a_1_to_m
from proveit.logic import And, CartProd, Equals, InSet
from proveit.logic.sets.cartesian_products import a_in_A__1_to_m

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([x, A_1_to_m, a_1_to_m], Equals(InSet(x, CartProd(A_1_to_m)), And(Equals(x, [a_1_to_m]), a_in_A__1_to_m)).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(\left(x, A_{1}, A_{2}, \ldots, A_{m}, a_{1}, a_{2}, \ldots, a_{m}\right) \mapsto \left(\begin{array}{c} \begin{array}{l} \left(x \in \left(A_{1} \times  A_{2} \times  \ldots \times  A_{m}\right)\right) =  \\ \left(\left(x = \left(a_{1}, a_{2}, \ldots, a_{m}\right)\right)\land \left(a_{1} \in A_{1}\right) \land  \left(a_{2} \in A_{2}\right) \land  \ldots \land  \left(a_{m} \in A_{m}\right)\right) \end{array} \end{array}\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: 2 body: 3
2	ExprTuple	19, 18, 23
3	Operation	operator: 15 operands: 4
4	ExprTuple	5, 6
5	Operation	operator: 24 operands: 7
6	Operation	operator: 8 operands: 9
7	ExprTuple	19, 10
8	Literal
9	ExprTuple	11, 12
10	Operation	operator: 13 operands: 14
11	Operation	operator: 15 operands: 16
12	ExprRange	lambda_map: 17 start_index: 27 end_index: 28
13	Literal
14	ExprTuple	18
15	Literal
16	ExprTuple	19, 20
17	Lambda	parameter: 34 body: 21
18	ExprRange	lambda_map: 22 start_index: 27 end_index: 28
19	Variable
20	ExprTuple	23
21	Operation	operator: 24 operands: 25
22	Lambda	parameter: 34 body: 29
23	ExprRange	lambda_map: 26 start_index: 27 end_index: 28
24	Literal
25	ExprTuple	30, 29
26	Lambda	parameter: 34 body: 30
27	Literal
28	Variable
29	IndexedVar	variable: 31 index: 34
30	IndexedVar	variable: 32 index: 34
31	Variable
32	Variable
33	ExprTuple	34
34	Variable