Expression of type ExprTuple

from the theory of proveit.logic.sets.intersection

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
from proveit.logic import Equals, InSet, Intersect
from proveit.logic.sets import x_in_every_A

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