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, x
from proveit.logic import Forall, InSet
from proveit.logic.sets import basic_comprehension_y

# build up the expression from sub-expressions
expr = Lambda([S, Q], Forall(instance_param_or_params = [x], instance_expr = InSet(x, S), domain = basic_comprehension_y))

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[\forall_{x \in \left\{y~|~Q\left(y\right)\right\}_{y \in S}}~\left(x \in S\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	27, 25
2	Operation	operator: 3 operand: 5
3	Literal
4	ExprTuple	5
5	Lambda	parameter: 12 body: 7
6	ExprTuple	12
7	Conditional	value: 8 condition: 9
8	Operation	operator: 23 operands: 10
9	Operation	operator: 23 operands: 11
10	ExprTuple	12, 27
11	ExprTuple	12, 13
12	Variable
13	Operation	operator: 14 operand: 16
14	Literal
15	ExprTuple	16
16	Lambda	parameter: 28 body: 17
17	Conditional	value: 28 condition: 18
18	Operation	operator: 19 operands: 20
19	Literal
20	ExprTuple	21, 22
21	Operation	operator: 23 operands: 24
22	Operation	operator: 25 operand: 28
23	Literal
24	ExprTuple	28, 27
25	Variable
26	ExprTuple	28
27	Variable
28	Variable