Expression of type ExprTuple

from the theory of proveit.logic.sets.comprehension

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, ExprRange, ExprTuple, IndexedVar, Lambda, S, Variable, n, x, y
from proveit.core_expr_types import Q__y_1_to_n, f__y_1_to_n, y_1_to_n
from proveit.logic import And, Equals, InSet
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Lambda([y_1_to_n], Conditional(Equals(x, f__y_1_to_n), And(ExprRange(sub_expr1, InSet(IndexedVar(y, sub_expr1), IndexedVar(S, sub_expr1)), one, n), Q__y_1_to_n))))

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(y_{1}, y_{2}, \ldots, y_{n}\right) \mapsto \left\{x = f\left(y_{1}, y_{2}, \ldots, y_{n}\right) \textrm{ if } \left(y_{1} \in S_{1}\right) ,  \left(y_{2} \in S_{2}\right) ,  \ldots ,  \left(y_{n} \in S_{n}\right) ,  Q\left(y_{1}, y_{2}, \ldots, y_{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	parameters: 16 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12
9	Variable
10	Operation	operator: 13 operands: 16
11	ExprRange	lambda_map: 14 start_index: 22 end_index: 23
12	Operation	operator: 15 operands: 16
13	Variable
14	Lambda	parameter: 29 body: 17
15	Variable
16	ExprTuple	18
17	Operation	operator: 19 operands: 20
18	ExprRange	lambda_map: 21 start_index: 22 end_index: 23
19	Literal
20	ExprTuple	25, 24
21	Lambda	parameter: 29 body: 25
22	Literal
23	Variable
24	IndexedVar	variable: 26 index: 29
25	IndexedVar	variable: 27 index: 29
26	Variable
27	Variable
28	ExprTuple	29
29	Variable