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, m, x
from proveit.core_expr_types import A_1_to_m
from proveit.logic import Equals, Forall, InSet, Intersect, NotInSet
from proveit.logic.sets import x_notin_some_A
from proveit.numbers import NaturalPos

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(m, Conditional(Forall(instance_param_or_params = [x, A_1_to_m], instance_expr = Equals(NotInSet(x, Intersect(A_1_to_m)), x_notin_some_A)), InSet(m, NaturalPos))))

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(m \mapsto \left\{\forall_{x, A_{1}, A_{2}, \ldots, A_{m}}~\left(\left(x \notin \left(A_{1} \cap  A_{2} \cap  \ldots \cap  A_{m}\right)\right) = \left(\left(x \notin A_{1}\right) \lor  \left(x \notin A_{2}\right) \lor  \ldots \lor  \left(x \notin A_{m}\right)\right)\right) \textrm{ if } m \in \mathbb{N}^+\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: 30 body: 3
2	ExprTuple	30
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	30, 11
10	Lambda	parameters: 12 body: 13
11	Literal
12	ExprTuple	33, 26
13	Operation	operator: 14 operands: 15
14	Literal
15	ExprTuple	16, 17
16	Operation	operator: 31 operands: 18
17	Operation	operator: 19 operands: 20
18	ExprTuple	33, 21
19	Literal
20	ExprTuple	22
21	Operation	operator: 23 operands: 24
22	ExprRange	lambda_map: 25 start_index: 29 end_index: 30
23	Literal
24	ExprTuple	26
25	Lambda	parameter: 37 body: 27
26	ExprRange	lambda_map: 28 start_index: 29 end_index: 30
27	Operation	operator: 31 operands: 32
28	Lambda	parameter: 37 body: 34
29	Literal
30	Variable
31	Literal
32	ExprTuple	33, 34
33	Variable
34	IndexedVar	variable: 35 index: 37
35	Variable
36	ExprTuple	37
37	Variable