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 Conditional, ExprTuple, Lambda, x
from proveit.core_expr_types import A_1_to_m
from proveit.logic import 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], Conditional(x_in_every_A, InSet(x, Intersect(A_1_to_m)))))

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\{\left(x \in A_{1}\right) \land  \left(x \in A_{2}\right) \land  \ldots \land  \left(x \in A_{m}\right) \textrm{ if } x \in \left(A_{1} \cap  A_{2} \cap  \ldots \cap  A_{m}\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: 2 body: 3
2	ExprTuple	21, 15
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 16 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	21, 10
9	ExprRange	lambda_map: 11 start_index: 19 end_index: 20
10	Operation	operator: 12 operands: 13
11	Lambda	parameter: 25 body: 14
12	Literal
13	ExprTuple	15
14	Operation	operator: 16 operands: 17
15	ExprRange	lambda_map: 18 start_index: 19 end_index: 20
16	Literal
17	ExprTuple	21, 22
18	Lambda	parameter: 25 body: 22
19	Literal
20	Variable
21	Variable
22	IndexedVar	variable: 23 index: 25
23	Variable
24	ExprTuple	25
25	Variable