Expression of type Conditional

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, S, Variable, n, x, y
from proveit.core_expr_types import Q__y_1_to_n, R__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 = 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\{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()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

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