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, Qx, S, x
from proveit.logic import And, InSet
from proveit.logic.sets import basic_comprehension_y

# build up the expression from sub-expressions
expr = Conditional(InSet(x, basic_comprehension_y), And(InSet(x, S), Qx))

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 \left\{y~|~Q\left(y\right)\right\}_{y \in S} \textrm{ if } x \in S ,  Q\left(x\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: 20 operands: 3
2	Operation	operator: 16 operands: 4
3	ExprTuple	13, 5
4	ExprTuple	6, 7
5	Operation	operator: 8 operand: 12
6	Operation	operator: 20 operands: 10
7	Operation	operator: 22 operand: 13
8	Literal
9	ExprTuple	12
10	ExprTuple	13, 24
11	ExprTuple	13
12	Lambda	parameter: 25 body: 14
13	Variable
14	Conditional	value: 25 condition: 15
15	Operation	operator: 16 operands: 17
16	Literal
17	ExprTuple	18, 19
18	Operation	operator: 20 operands: 21
19	Operation	operator: 22 operand: 25
20	Literal
21	ExprTuple	25, 24
22	Variable
23	ExprTuple	25
24	Variable
25	Variable