Expression of type Lambda

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, ExprRange, IndexedVar, Lambda, S, Variable, n, x, y
from proveit.core_expr_types import Q__y_1_to_n, R__y_1_to_n, y_1_to_n
from proveit.logic import And, InSet
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda([y_1_to_n], Conditional(InSet(x, R__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(y_{1}, y_{2}, \ldots, y_{n}\right) \mapsto \left\{x \in R\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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 14 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 17 operands: 4
3	Operation	operator: 5 operands: 6
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 10
7	Variable
8	Operation	operator: 11 operands: 14
9	ExprRange	lambda_map: 12 start_index: 20 end_index: 21
10	Operation	operator: 13 operands: 14
11	Variable
12	Lambda	parameter: 27 body: 15
13	Variable
14	ExprTuple	16
15	Operation	operator: 17 operands: 18
16	ExprRange	lambda_map: 19 start_index: 20 end_index: 21
17	Literal
18	ExprTuple	23, 22
19	Lambda	parameter: 27 body: 23
20	Literal
21	Variable
22	IndexedVar	variable: 24 index: 27
23	IndexedVar	variable: 25 index: 27
24	Variable
25	Variable
26	ExprTuple	27
27	Variable