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, S
from proveit.logic import SubsetEq
from proveit.logic.sets import basic_comprehension_y

# build up the expression from sub-expressions
expr = Lambda([S, Q], SubsetEq(basic_comprehension_y, S))

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