Expression of type Conditional

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, IndexedVar, S, Variable, n, x
from proveit.core_expr_types import R__x_1_to_n, f__x_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(f__x_1_to_n, And(ExprRange(sub_expr1, InSet(IndexedVar(x, sub_expr1), IndexedVar(S, sub_expr1)), one, n), R__x_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\{f\left(x_{1}, x_{2}, \ldots, x_{n}\right) \textrm{ if } \left(x_{1} \in S_{1}\right) ,  \left(x_{2} \in S_{2}\right) ,  \ldots ,  \left(x_{n} \in S_{n}\right) ,  R\left(x_{1}, x_{2}, \ldots, x_{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: 3 operands: 10
2	Operation	operator: 4 operands: 5
3	Variable
4	Literal
5	ExprTuple	6, 7
6	ExprRange	lambda_map: 8 start_index: 16 end_index: 17
7	Operation	operator: 9 operands: 10
8	Lambda	parameter: 23 body: 11
9	Variable
10	ExprTuple	12
11	Operation	operator: 13 operands: 14
12	ExprRange	lambda_map: 15 start_index: 16 end_index: 17
13	Literal
14	ExprTuple	19, 18
15	Lambda	parameter: 23 body: 19
16	Literal
17	Variable
18	IndexedVar	variable: 20 index: 23
19	IndexedVar	variable: 21 index: 23
20	Variable
21	Variable
22	ExprTuple	23
23	Variable