Expression of type Lambda

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, Lambda, 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 = Lambda(x, 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())

x \mapsto \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()

no style options

# display the expression information
stored_expr.expr_info()

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