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

# build up the expression from sub-expressions
expr = Lambda([S, Q, x], Equals(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(S, Q, x\right) \mapsto \left(\left(x \in \left\{y~|~Q\left(y\right)\right\}_{y \in S}\right) = \left(\left(x \in S\right) \land Q\left(x\right)\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: 1 body: 2
1	ExprTuple	28, 26, 17
2	Operation	operator: 3 operands: 4
3	Literal
4	ExprTuple	5, 6
5	Operation	operator: 24 operands: 7
6	Operation	operator: 20 operands: 8
7	ExprTuple	17, 9
8	ExprTuple	10, 11
9	Operation	operator: 12 operand: 16
10	Operation	operator: 24 operands: 14
11	Operation	operator: 26 operand: 17
12	Literal
13	ExprTuple	16
14	ExprTuple	17, 28
15	ExprTuple	17
16	Lambda	parameter: 29 body: 18
17	Variable
18	Conditional	value: 29 condition: 19
19	Operation	operator: 20 operands: 21
20	Literal
21	ExprTuple	22, 23
22	Operation	operator: 24 operands: 25
23	Operation	operator: 26 operand: 29
24	Literal
25	ExprTuple	29, 28
26	Variable
27	ExprTuple	29
28	Variable
29	Variable